If the tap’s dripping it probably needs a new washer. To replace it, turn off the water supply and turn the tap fully on. Place a plug in the plughole to avoid losing small parts.
On a non-rising spindle tap, prise off the handle cover to expose the retaining screw. Remove the screw and handle to expose the headgear.
On a rising spindle tap, first remove the coloured index disc on the handle and the retaining screw to release the handle.
Step 1. Remove the headgear
Remove the headgear after you have taken off the handle, using an adjustable wrench to undo the headgear nut. Brace the tap with your other hand to stop it from spinning as you turn the nut, as this could weaken the tap’s plumbing connection.
Step 2. Lever off old washer
Lever off the old washer with a screwdriver and replace the body washer and spindle O-ring using needlenose pliers. If the
leak persists, the valve seat may need to be resurfaced. If in doubt, contact a plumber.