The Zhentarim might expel you, or worse
It's understandable to be unsure what would happen in this situation. After all, it's hard to predict how an organization that values ruthlessness and personal achievement will view those values when directed against one of their own members.
The honest answer is that your DM will have to decide. There may be members of the Zhentarim who would reward a carefully managed (and subtly hidden) assassination of certain of their own members: perhaps if the murdered member had been very unpopular, unprofitable, or had been a traitor to the organization? But don't expect that response: you could definitely be expelled for killing a fellow member. Or they could take a more... permanent approach to the problem.
The reason it's hard to know what to expect is found in the central Beliefs of the Zhentarim (findable on their faction overview).
The Zhentarim is your family. You watch out for it, and it watches out for you.
You are the master of your own destiny. Never be less than what you deserve to be.
Everything—and everyone—has a price.
Naturally, these beliefs could be defined or prioritized differently by different individuals, but they give the broad strokes of how a member of the Zhentarim is expected to act. So how the Zhentarim react to you may depend on how much your action upholds or violates these beliefs. But depending on a couple of factors, these beliefs might be seen to defend or condemn one member murdering another.
1.) Did you "watch out for the Zhentarim" by killing one?
This depends on why you did it. If you killed a Zhentarim member for betraying the faction, then probably you didn't violate this tenet. But if you killed them to stop them from robbing a friend of yours, you're probably in trouble. If you can claim that your actions overall helped the Zhentarim, that'll help your case.
2.) Were you trying to "be what you deserve to be"?
Maybe you killed this Zhentarim for selfish reasons: trying to rob them, or take their place in the Zhentarim heirarchy. Although this would definitely seem to violate belief #1 above, it might be defensible as upholding belief #2: that you won't let anyone (even fellow members) force you to be "less than what you deserve to be." Depending on how the Zhentarim prioritize their beliefs, you might be able to defend your actions by this tenant.
Of course, that doesn't mean you'll be in the clear, because...
3.) Everything has a price
If you killed selflessly in the defense of the Zhentarim, you could defend what you did by belief #1. If you killed selfishly in the name of yourself, you could defend what you did by belief #2. But either way, that doesn't mean you'll get off scot free, because "everything has a price."
By killing a person the Zhentarim decided to welcome into their ranks, you've stolen something from the organization as a whole. Everything that person ever would have done for the Zhentarim will now never be done: everything they would have given to "take care of" their Zhentarim family will never be given.
You'll need to somehow make up that balance. Maybe you could try and argue that the act of killing him balances the books in-and-of itself: if he was a traitor, or dead weight, you might feel that killing him made the organization stronger. But taking it upon yourself to make that decision, without consulting any other members, is likely to have a price of its own: after all, if anyone in the organization can just decide to kill any other member when they want, what does belief #1 even mean?
What kind of faction is this?
Ultimately, how the Zhentarim react to this murder will not only depend on your justification or reasons for committing it: it will also depend on how your DM views the Zhentarim, and how unusual it was for this to happen in the DM's version of the faction. Maybe your DM views the Zhentarim as an ultimate Darwinian free-for-all: a Sith like organization where the culling of weak members is not only tolerated but encouraged. In that case, you may be in the clear. But if your DM views the Zhentarim as a group that looks after its own, that protects both its members and its reputation, and that would only permit the killing of one of its members for a serious infraction (like, say, killing one of its members)...
Well, you may need to prepare yourself for the worst. After all, the Zhentarim are a family. You were the master of your own destiny. And everything has a price.