Basic Trope: A non-human individual has a principle of not killing a member of his same species
Straight: The ape Brutus is about to kill the ape Caesar, but refuses, because he won't kill a fellow ape.
Exaggerated: Ape Brutus shall not kill ape Caesar... and neither fight with him, insult him, or do anything unpleasant to him.
Downplayed: Ape Brutus shall never kill ape Caesar... but nobody said anything about breaking his legs.
Humans kill each other for any petty reason, and they are the real monsters. Apes do not want to be like them.
Apes are very hot-headed and have long memories; a murder could quickly devolve into a protracted and destructive blood feud.
Inverted: Apes do not kill humans, but will gladly kill fellow apes.
The ape Brutus is about to kill ape Caesar. He stops, remembers that ape shall never kill ape... and says "But, in your case, I'll make an exception!"
Apes have strong taboos against killing members of their own race, but this only applies to direct killings. Numerous humans and other species find work as assassins in the Ape Confederacy, "resolving" disputes between apes.
The ape Brutus is about to kill ape Caesar. He stops, remembers that ape shall never kill ape, and says "But, in your case, I'll make an exception!". But he did not really kill him, he misses the attack on purpose making it seem for a moment as if he did it, and gives a lecture on the other apes behind who were asking for blood.
...But it turns out the hiring of assassins is actually highly illegal, and any ape who is discovered to have done so is incarcerated or exiled.
Parodied: Ape Brutus shall never kill ape Caesar... "Hey, who are you calling "ape"! I told you, I'm an alien that only looks like a Terran ape!" "Oh, goody, then you're fair game!"
Averted: The high priest proudly tells the visitors that ape's don't kill each other. Then we see a riot outside the temple, and the police apes are killing the ape rioters without problem.
Enforced: The author is living in a civil war in the real world, and wants to point how bad it is to kill fellow people, by using a fictional race as a metaphor.
Lampshaded: Brutus has Caesar at his mercy: "You'll live, but only because I'm not in the mood to have discussions with those dammed priests and their precious 'Ape shall never kill ape' ancient rules!"
The founders of the Ape Confederacy pass down strict laws against killing other apes, hoping to prevent the devastating civil wars they used to go through.
Apes have a very low fertility rate, so low that the losses due to even an extremely low homicide rate would be unsustainable.
Exploited: Ape Brutus is about to kill ape Caesar, who reminds him about the rule.
Ape Brutus shall not kill ape Caesar... but, fortunately, his human sidekick does not have such moral concerns.
An ape priest loudly recites the commandment to not kill other apes before a large crowd... and is promptly gunned down by an ape in the back of the crowd, sparking a riot.
Conversed: "They won't kill other apes, but they'll slaughter humans by the thousand? Yeah, these guys are real moral."
Played for Laughs: Ape Brutus kills a human, only to remove his mask and discover he's an ape! Oh, no! Hey wait, he was wearing a second mask beneath the mask: he's actually a lizard-like alien!
Played for Drama: While slaughtering humans, Brutus accidentally kills Caesar, an ape who was nearby. He is filled with remorse for breaking the sacred oath, and becomes an outcast from ape society.