No this is not the tense required after that sort of conditional.


He would kill him if he had the chance.


This is a simple present- a timeless fact.
And
It is not a conditional fact - it sets up the condition.
The desire is always there (hidden, "in the harbour"). The action only happens if the condition is met.

He harbours a desire to kill him.

He will kill him if he gets a chance.
He would kill him if he ever got the chance.

It looks OK to me (though I would probably put a comma after "Peter" - I don't know if there's any rule to explain it other than "that's where I pause when I say the sentence).

"Harbours a desire" is definite, it's true, not conditional - so the condition of "having the opportunity" must refer to the infinitive "to kill Peter".

Another (possibly slightly more formal) wording could be:
"John harbors a desire to kill Peter, were he to have the opportunity to do so."

But I'd say "John'd like to kill Peter if he had the chance" - which is very like your ORIGINAL sentence.
I think that the difference is that your original one - "John harbors a desire to kill Peter if he had the opportunity to do so" - uses very formal wording ("harbouring a desire", "having the opportunity" and "to do so") with a very informal construction using "had".

Your later one - "John harbors a desire to kill Peter should he have the opportunity to do so" - uses the formal phrases with the formal subjunctive "should he have".

My offering - "John'd like to kill Peter if he had the chance" - is all informal.

Both the fully formal and the fully informal ones sound OK - it's the mixture which doesn't seem to work.