This is the 636th most frequent Czech word.
trenéra
The Czech word "trenéra" means "coach" or "trainer" (in the genitive or accusative singular form).
Here, 'trenérem' is the instrumental case of 'trenér', used to show the role or profession someone has assumed.
Můj bratr se stal trenérem místního fotbalového týmu.
My brother became the coach of the local football team.
In this sentence, 'trenérem' is again in the instrumental case, indicating the role that someone is to take on.
Požádali mě, abych se stal jejich trenérem.
They asked me to become their coach.
Here, 'trenérovi' is the dative case of 'trenér', indicating the person towards whom an action is directed.