Yes.
There is no reason that someone cannot hold a personal driving licence because they have a pacemaker.
Usually we would recommend that driving is not restarted until six weeks after the insertion of a first pacemaker. You should also inform both your car insurance company and the DVLA that you have had a pacemaker inserted.
When travelling in a car immediately after the insertion of a pacemaker you should be careful of the seat belt over the site of the skin wound. In the two to three weeks after the insertion of a new system you should also be particularly careful in reaching up to pull the seat belt into position as this can cause movement of the wires. This is only a problem during this time as after this the wires become very stable and all normal physical activities are fine.