If you want to use your driving licence in Germany, it will depend on the country where you are a citizen.
The following applies for people who are not from the EU, Liechtenstein, Norway or Iceland: You can use your driving licence in Germany for six months. After that, you need a German driving licence. It may be that you will have to take another exam for this, depending on which country you got your driving licence in. You can find more information at your town’s driver licensing authority ("Fahrerlaubnisbehörde").
Never drive without a valid driving licence. That is a criminal offence and could put your asylum application ("Asylantrag") at risk.