Calvin didn’t like HIDING IN HIS BEST FRIEND'S SCUMMY BASEMENT. BUT it wasn’t even an hour ago that Calvin's rivals and so-called protectionists had blown his restaurant apart, AND THE BASEMENT SHOULD BE SAFE.

"Calvin didn’t like this bar, he didn’t like it at all."

I believe that you need either a period of semi-colon between he and bar. I would go with a period. I think it puts the emphasis in the right place.

Otherwise, good opening sentence. It already creates tension. What's he doing ina bar he doesn't like? Why doesn't he like it? Good questions to have going through my mind.

" It was dark, stuffy, smelly, and scummy, mostly scummy."

If you keep this sentence, I think that you need a '--' between scummy and mostly scummy. But I'm not sure if this is a good follow-up to what you had before. For one thing, it doesn't give me any new information. For another thing, this is a good example of "telling" -- I'm sure you've heard "show don't tell." Well, here you are, telling me that a bar is dark, stuffy, smell, and scummy. If this is important, I'd rather see it more clearly.

" He would never tell Greg, the owner, though. Best friends didn’t dothat to each other. "

Interesting and not where I had expected this to go.

"He only sought sanctuary, he wouldn’t be here if he wasn’t. It wasn’t even an hour ago that his rivals and so-called protectionists had blown his restaurant apart. "

This is where you lost me but it shouldn't have been. This is the story problem. This is your hook. For one thing, I'm not sure what you mean by "so-called protectionists" and it's bugging me. For another, I think you could have said all this in a much, much shorter paragraph. I think it could have all been one sentence, without nearly as many was's. (I'm not the "to be" police or anything, but being creates a sense of standing still and this is a part of the story that I think you would much rather see moving.)

"His hand shook as he saw blood from a bullet wound seep through layer upon layer of cloth."

Doesn't he feel the bullet, too? I would like more detail about this from his point of view. Try to add sensory details -- not just sight but smell, taste, sound, and texture.

" Next to him on the counter was his clarinet, his prized possession and only connection he had to his past."

Suggestions: reword to remove the was. Otherwise, another good detail. I expect the clarinet to be important in this story.

" Next to that sat a half-empty glass of scotch; he wasn’t a drinker but this was not normal circumstances."

Should either read "this was not a normal circumstance" or "these were not normal circumstances." (verb-subject confusion) I also think a period would work better than the semi-colon here, but that's just because I like the stacato of short sentences driving forward tension.

" The low light in the bar cast a reflection on the polished surface of the counter."

I don't expect to see polished counters in a scummy bar.

" The face looking back at him was pale and drained"

Calvin gulped a shot of scotch. He wasn't a drinker and his stomach clenched in protest. The joint reeked of stale smoke, sweat and the metallic smell of blood that oozed up and soaked through the cloth over his bullet wound. He was nauseous and fought off the urge to puke.
"The restaurant..." he said to Greg.
"The restaurant?"
"The restaurant. The bastards blew my restaurant."

"...these were not normal circumstances."

Yes, but don't we know that from the info you have already given?

The word "scummy" - might be just me, but this has a "high school" feel to it - a word more likely to be used by kids. I don't think the word fits in with this scene.

If you mention the first time we see the character that he is bleeding, the reader's natural question is "What happened?" If you don't answer that question in the next lines, you are withholding. If the reader was "there" when he was shot, saying he's now bleeding isn't withholding.

If he's in a bar, the reader might not ask why. If he's hiding out in a bar, the reader wants to know why. Establish the scene before you move into the next details.

Don't try to cram everything in the first 13 lines because you will fail regardless of how amazing a writer you are.

So as an example, the italics are my thoughts as reader:

Calvin didn’t like this bar.
Which bar?

He didn’t like it at all.

Okay, I know that already. So why is he there if he really hates it

It was dark, stuffy, smelly, and scummy... mostly scummy.

EWWWW. Wait, how is it scummy? Why are we here?

He would never tell Greg, the owner, though.

Tell him what? Oh, it's GREG's bar.

Best friends didn’t do that to each other.

Oh, they are best friends. Cool. But wait why wouldn't he tell the truth?

He only sought sanctuary, he wouldn’t be here if he wasn’t.

Sanctuary? Why does he need sanctuary? Visions of The Hunchback in Notre Dame yelling "Sanctuary!"

It wasn’t even an hour ago that his rivals had blown his restaurant apart.

Oh, that's why he needs to hide. Why did "they" blow the restaurant apart and who are "they?"

Making me ask questions is good, making me wait for answers is less so.

Consider this as an alternative:

Calvin didn't like Greg's bar. It stank of spilled beer. But he'd known Greg all his life and Greg was the only one he was sure wouldn't turn him into the _____ gang for the reward on his head."

The next thing I'd want to know is why the gang is after him.

You might be starting in the wrong place. As a rule of thumb you start just before the MC's life falls apart. We start this story an hour after it happens. Could you start in Calvin's restaurant before it gets blown to heck?