I have a residence card but I would like to work for another employer. Do I need to wait for my current residence permit/residence card to be withdrawn?

You do not have to wait for your permit to be withdrawn. Make sure to apply for a new residence and work permit, as soon as possible. Remember that you are not allowed to work for your new employer on the basis of your residence card without a valid work permit (unless you hold another document entitling you to work for your new employer, such as a declaration on entrusting work to a foreigner or a work permit.