Whether or not you can work while waiting for your next residence permit depends on the kind of residence permit you had previously. Generally, if your last residence permit granted you the right to work in Germany then you can keep working until your permit is renewed or a new one is issued. If you come from a country that has a visa-free entry agreement with Germany, then you shouldn’t have a problem re-entering the country, even while waiting for a new visa, and then you can stay as you wait for your residence permit to be extended.