Como dizer ''Render alguém no posto de trabalho'' em inglês

"Vou render meu colega no posto de vigia."
I will be handing over the watch to the guy replacing me. (from the 'military' when handing over the watch or station).
I'll be passing the shift to the next guy/nurse/doctor, etc.
Passing the baton.../pass the torch...(a bit colloquial/slangy).

, ou "Aonde vou pegar minha rendição ao fim da jornada?"
Where do I meet/find the next shift person?.../the next shift person to replace me?

"Fui rendido às 21h".
I handed over/handed off the shift (to the next employee) at 9 o'clock PM.
The guy took over the shift on around 9 o'clock, then I left.
It was nine o'clock when the/my shift changed.

I hope this helps!

I would say "replace" would be more to the point, "relieve" doesn't sound natural English for me.
Even so (in this context) it's advisable to be careful, I wouldn't say "my replacement" for instance, but in the sentence I offered "replace" was used by way of definition. Replacement would be use in some cases as "cover" the guy that will cover your shift since you have asked him (or have dealt in some way)...
Replacement - in less temporary basis, can be your "substituto" (numa função), could be because you are retiring or leaving for vacation.

Os verbos RELIEVE e REPLACE, são comuns e equiparados ao RENDER (substituir)!