A licensed plumber means the person completed the necessary education or training required to work as a professional tradesperson. Hiring a licensed plumbing service means the people working on your building are knowledgeable about water and gas pipes. If you use unlicensed workers, you run the risk of them damaging your home even further and endangering you by doing faulty work.
Sometimes a faucet leak can be stopped by replacing the rubber washer at the end of a faucet stem or cartridge. This is a more common repair on older fixtures when things were built to last and designed to be able to be maintained. Other times the whole stem or cartridge needs replacement or the bibb seat deeper back into the fixture needs replacement. That leads to matching up the right components and often times making a trip to the hardware store or plumbing supply house necessary due to the many varieties, makes and models of faucets. My advice is to make sure your Plumber has faucet repair kit on their truck before having them come out to assess the issue.