Arahbo, Roar of the World

Once either of Arahbo's triggered abilities has resolved, the affected Cat keeps its bonus even if Arahbo changes zones later in the turn.

This commander's eminence ability is a triggered ability. The commander must be on the battlefield or in the command zone as the trigger event occurs and also as the triggered ability resolves. If the commander is in an appropriate zone as the trigger event occurs but leaves that zone, the ability won't do anything as it resolves.

Notably, if your commander is on the battlefield and its eminence ability triggers, but it's put into the command zone before that ability resolves, that ability won't do anything as it resolves. This is because an object that changes zones is considered a new object.