The night was dark and quiet; a few cars passed by on a street that was generally busy during the daytime, the sound of the motors fading in and growing to a dull roar, then fading out as they left the other way, only stopping occasionally as the light changed. A tall, slim figure stood leaning against a building, watching the road with eyes unseen, looking out from underneath a dark cowl. He was waiting.
As he stood, the sound of a car approaching rose into the air from down the street off to his right. At around the same moment, another pair of headlights appeared from the street directly ahead of the figure. One of them was moving at a normal pace, a steady thirty-five miles per hour, right at the speed limit. The other was not; nor was it moving in a

A tall, slim figure stood leaning against a building, watching the road with eyes unseen, looking out from underneath a dark cowl. He was waiting Who's POV is this? How do we know he's waiting? Who are his eyes hidden from? At the moment this feels very distant when you need to be involving the reader in the story, pulling them in from the get-go.

At the moment I probably wouldn't read on, it feels so distant that I'm too removed from the story to be interested in a car travelling at a steady thirty-five miles an hour, or that another car is coming from another direction. Maybe if you plunge us into the POV of the shadowy figure and give us a hint of what he's waiting for I'll be more hooked.

Good luck with it!

A tall slim figure stood leaning against a building, watching the road with eyes concealed by a cowl. He was waiting...

This is very distant because it is third person, across the street POV. Then, all of a sudden, we have access to some knowledge about his intimate thoughts and motives, like the camera has snapped from the distant shot to into the middle of his ear. And all this before we know who this person is.

He knew his services would be needed in a few minutes. Every few moments he glanced at an hourglass, the sand quickly rushing into the bottom half...

I like the imagery of the hourglass, but the line before it only prompted the question, why was death waiting? Surely he had many people to process in the time that he waited. Furthermore, that line makes us feel told, when the same information is gained in the second sentence. Show, don't tell is an overused mantra, but these two sentences show up the impact of the concept.

As he stood, the sound of a car approaching rose into the air from down the street off to his right...

I would encourage you to work more on defining the POV clearly in your own mind, and showing us what the POV character sees. Right now I think you're telling when showing would be better. Also, there are inconsistencies--each in itself small but which collectively made me pause and ultimately would stop me reading on.

For example, "The night was dark and quiet": we know night is dark. What is it about this night's darkness that makes it worth mentioning? Are the street lights out? No moon? Also, that it's quiet is contradicted by the second part of the sentence.

"a normally busy street." I think this is telling us something that either Death or the narrator knows, and it doesn't help us visualize the scene. Busy with what--shoppers? Hookers? Street traders? Drunken revellers? Tramps and drug dealers? If you show us what the POV character sees--shops, theatres, empty bars, derelict buildings, whatever--we'll be able to see it too. As it is, we see a generic night street scene, perhaps the scene in your mind, perhaps not, and either way, we're not immersed.

One assumes the tall slim figure is Death, but since the POV seems shaky, it's not certain; Death could be observing the tall slim figure. Assuming they're one and the same character I'd recommend considering starting with the hooky "Death hated his job", rooting the POV firmly in Death, and showing us the street scene as he experiences it in sights, sounds, even smells. If his appearance is important, I guess he'll have to admire himself in a shop window or something. (And BTW, if his eyes are concealed by a cowl, how does he see?)

I like the imagery of an hour glass but wonder how he'd carry it around with him. "quickly rushed": delete "quickly", redundant.

I imagine he's standing at an intersection, but this isn't clear--he's watching a road, not an intersection. How does he know the speed of one car is exactly 35 mph--and does it matter? One assumes that the salient point is that one car is approaching at a normal speed, the other speeding. But if exact speed is something Death knows because of his privileged status, I think it should be hinted at somehow.

"the sound of a car approaching rose into the air from down the street off to his right": I don't think sounds rise into the air and thought for a moment the car was flying. (SF readers can be very literal-minded.) And, the last part could be simplified, perhaps "from the street to his right".

///The night was dark and quiet, with only a few cars passing on a normally busy street.///

Your first sentence doesn't do anything. If the way you write requires you start off with a bit of filler to set the stage in your mind that's fine, just remember to go back and delete it when once you're rolling and then add back any critical information somewhere after the hook.

///A tall[,] slim figure stood leaning against a building, watching the road with eyes concealed by a cowl. He was waiting, powerless to stop the events that were about to unfold.///

You could start off here, but go ahead and call it Death right away. The mystery of "who is the tall, slim figure?" isn't a hook to begin with, and you make your reveal 2 sentences later anyway. Readers like to get a name right off the bat so they can tag the character they're following. Also, consider - if his eyes are concealed by his cowl, how can he watch the road? Finally, if your story is going to involve some sort of rebellion by Death against his job, then describing him as powerless is wrong - he only feels powerless at this moment.

///Death hated his job. Day after day it was the same depressing duty from which there was no relief. He knew his services would be needed in a few minutes.///

You're starting to dip into Death's POV here, which is good. The note about the reaper hating his job is a touch cliche, but it's a tried-and-true hook ("Mort" by Terry Pratchett probably does it best). The followup line is weak. Take us a little deeper and maybe give us a direct thought or two to cement the POV.

///Every few moments he glanced at an hourglass, the sand quickly rushing into the bottom half.///

You use "few minutes" and "few moments" in back to back sentences. I didn't like the rhythm of that. Also, where is the hourglass? Is he holding it? Does that mean he could flip it over? Will it tie up his hands later when he uses the scythe? Or can he keep it in his cloak? I think others have mentioned this. If you keep the hourglass, consider adding to the tension with a short sentence about the limited amount of sand in the upper half.

///As he stood, the sound of a car approaching rose into the air from down the street off to his right. At around the same moment, another pair of headlights appeared from the street directly ahead of him. One of them was moving at a normal pace, a steady thirty-five miles per hour, right at the speed limit.///

You don't need "As he stood", nor "At around the same moment". The lines work better and without those clauses. Keep your sentences active. "A sound rose" isn't as good as "Death heard the sound of". "Was moving" isn't as good as "drove" or "rolled". "Another pair of headlights" is awkward since there is no first pair of headlights, only a sound.

There's also the problem of helping the reader see the scene in their head. Give an adjective or a tiny (and I mean tiny) description of each car, so that when you tell us one is family sedan rolling along the highway, and the other is a muscle car tearing through the hills, we know what's what.

Death was waiting. He stood on the corner of an empty intersection, tapping his foot against the pavement, occasionally glancing at an hourglass held in one bony hand. The sand was rushing into the bottom chamber, with only a little remaining in the top.
It was a dark night around him. He wished it were also stormy; that way at least the mood would be properly set for what was about to happen. He knew his services would be needed in a few minutes, as they were constantly.
Death hated his job. Day after day it was the same depressing duty from which there was no relief, no change, and no reward. He’d rather be almost anywhere than standing here in the dark waiting for man to die. He wondered briefly what the other Horsemen of the Apocalypse were up to.

/// He stood on the corner of an empty intersection, tapping his foot against the pavement, occasionally glancing at an hourglass held in one bony hand. The sand was rushing into the bottom chamber, with only a little remaining in the top.///

I like the first two clauses. Lose "occasionally" in the third. You don't need the adverb and "glancing" conveys that on its own. You might also consider breaking the first sentence up and running the last clause with the second sentence. My own preference would be like this: "He stood on the corner of an empty intersection, tapping his foot against the pavement. Bone echoed on asphalt like the ticking of a watch until it was drowned out by the noise of an approaching car. He glanced at the hourglass in his hand. Its sand was almost gone; he would be needed soon." That might be darker than you're looking for and I'm sure you can do better, but I'm trying to provide an example of pushing things together so a lot can happen at once. Death is clearly bored - you get a visual of this rhythmic foot tapping (and it's a little macabre with the bone on asphalt note). You also know that a car is coming when the noise drowns out the echo of his foot tapping, and you can't help but make the connection that the driver is gonna die because he's approaching as the sands run out.

///It was a dark night around him. He wished it were also stormy; that way at least the mood would be properly set for what was about to happen. He knew his services would be needed in a few minutes, as they were constantly.///

To me, this is the weakest part of the passage. You're trying to get into his POV, but it doesn't work nearly as well as the next part.

///Death hated his job. Day after day it was the same depressing duty from which there was no relief, no change, and no reward. He’d rather be almost anywhere than standing here in the dark waiting for man to die. He wondered briefly what the other Horsemen of the Apocalypse were up to.///

The first two sentences here I think are the strongest in the passage, because you're in Death's POV. I would move "waiting" to before "in the dark" and cut "for the man to die". You might want to rework the part about the weather and bring it into this paragraph after "no reward." Something like "He had a particular distaste for it on clear, beautiful night like this. Storms were so much better for setting the mood."

One last note: re the four horsemen - if you haven't read Good Omens, at least get a synopsis, since it's a comedy and the four horsemen play a large role in the later chapters. If you want to generate some envy for Death, make it a "cold, clear night" to suggest a northerly locale, and let him speculate that he heard War was vacationing in the Caribbean again, Famine had taken up permanent residence at a fashion lounge in Paris, and Pestilence seemed to be involved in a lot of intercourse these days (har, har).

Those are my thoughts, for whatever they're worth. I do think you're making good progress - keep at it. And remember, if you disagree with us, it's YOUR story. You have to be happy with it; we'll keep quibbling you to death if you let us. Sorry for the pun.