Car inherited, what’s going on with the offices?

Vlt. can you help me. My dear father has now passed away and has inherited his car from my mother. But she gives it to me directly, wants me to drive it. The car is still insured, both were/are living in place X. I myself live in place Y with my own still registered car. Both places also have different road offices. Where do I have to start now? Don’t want to travel from office to office all the time. Do I have to or may I take out a new insurance policy?