Faucet drip after water shut off
Turning the water off and on and getting the air bubbles back out of the pipes often loosens up "crud" in the pipes. Some of that crud may be stuck in the sealing part of the valve.

Try opening it all the way and running for a while, perhaps removing the aerator first. You might get lucky and have it work free of the valve mechanism.

In many cases the "crud" is somewhat rusty. It's generally harmless but unappealing - however, if a chunk large enough lodges in the wrong place, it can cause problems.