I probably should wait until the adrenalin dies down, but I really like this first 13 better than anything I've tried so far with my Toka and Julie story. See what you think:

****************************************************************
Frustration swamped Julie when the saddle hit Blue Smoke’s back too hard. “Sorry,” she said and snugged the girth against the krega’s belly. Damn, damn, damn. How could Toka be so... Go ahead and say it. The word’s stupid, and it’s not the first time. No, it’s just the first time it could cost Toka his life.

She recalled that last confrontation with Degan. “Listen little girl,” he said. “You might be first officer on that starship of yours, but in Noramus the men rule and our women know their place.” Noramian women took care of the home, raised the children, and, most important of all, pleased their mate. Very few Noramian couples shared an equal partnership. Men made all the important decisions and the woman never opposed it, whether they agreed or not. One thing for sure: Noramus wasn’t Earth.
****************************************************************

Edited to add revised version:

****************************************************************
Frustration swamped Julie when the saddle hit Blue Smoke’s back too hard. “Sorry,” she said and snugged the girth against the krega’s belly. Damn, damn, damn. How could Toka be so... Go ahead and say it. The word’s stupid, and it’s not the first time. No, it’s just the first time it could cost Toka his life.

She recalled that last confrontation with Degan’s face just inches from hers and his index finger jabbed between her breasts. “Don’t you even think about trying anything when the time comes for me to take my rightful place as chief,” he said, “and that means getting rid of anyone in my way.”

He might not have come right out and said it, but his meaning was clear. Toka would be chief after his father. If anything happened to Toka, Degan would take his place if Julie
****************************************************************

There Is a lot going on here, maybe too much, because I am not really sure what I should be focusing on. I mean it seems to me that I should be focused on the "...first time it could cost Toka his life..." but then you skip on to what seems to me to be a different topic. I might be that Toka's problem is with Degan but that is not very clear if that is the case.

It just feels like you are trying to cram too much into this. To illustrate, in the first 13 lines you have Julie saddling some creature she has a telepathic link with. That means you have new species and telepathy that was not part of human society before. You have the introduction of Toka and he is in big trouble and not for the first time. The introduction of Degan who I assume is the antagonist, who for a start, does not seem to like women in authority. The introduction of a very male dominated society. You have the fact that Julie is a first office on a starship, which means despite the, I will call it backwardness of the afore mention male dominated society it is not universal and something that Julie is not used to dealing with. You tell us the name of the planet, and the fact that that planet is not Earth, but people do remember Earth well enough to reference the difference between the two. All good information, but as I said, so much that I just don't know what to focus on and it leaves me feeling a bit off balance.

I want to make it clear that I do like this, and despite everything I have said, I would keep reading.

*****
"Sorry," Julia muttered in frustration when the saddle hit Blue Smoke’s back again. She snugged the girth against the krega’s belly while lightly massaging the bruised area to comfort her ride. ...
*****

Then you jump into 3 same words in a row and a partial thought about Toka. I got lost here. I would start some motion, otherwise what is the purpose of a saddle.

The next paragraph has me completly lost: starship, couples, Earth - huh? There too much information and we know nothing about Degan except name. And you telling us to early about cutural differences (and not showing it).

Telling us about the male/female roles on this planet makes us forget about Toka’s life being in jeopardy. Unless Degan’s misogyny is the reason Toka’s in danger, this info is out of place. It is exactly the right place to introduce Degan, and hearing his own words in the form of a quote is great, it’s just what he’s saying.

IMO you need to give us two pieces of info in the second paragraph: why Degan has is in for Toka (or how Toka poked the bear), and why it’s going to be nearly impossible for her to save him. Degan’s distain for women might provide the latter, but on its own this info is non critical world building, good stuff, just not first thirteen stuff. Perhaps not even before the first crisis stuff. In the first rush after Toka is safe there is a little breathing room to explain more while you are setting up the next crisis.