If I want to obtain a residence card in connection with employment with a new employer, do I have to wait for the previous permit/card to be revoked?

You do not have to wait for the previous card to be invalidated, submit a new application for temporary residence and work as soon as possible. Remember, however, that you cannot work for a new employer without a valid permit! (unless you have a different title entitling you to work for a new employer - e.g. registered declaration on entrusting employment, work permit.)