Drip occurs when the faucet is closed; water leakage occurs when there is water flowing through the faucet. If you see water coming out of the handle, your tap is leaking; the first thing to do is to make sure the fill nut of the tap is tight, but be careful not to scratch the nut with a pliers or wrench.
Here are the tools you need to replace the faucet seal: adjustable wrench, replacement faucet seal, Vaseline.
If you find that the cause of the leak is not that the nut is loose, then you need to replace the seal. The sealing ring of the faucet may be a tight sealing ring composed of one or more O-shaped rubber rings, or something like a string or a soft metal wire wound around the cartridge under the packing nut.
When replacing the faucet seal, follow these steps:
Step 1: Turn off the water supply and remove the faucet handle.
Step 2: Unscrew the packing nut and remove the nut and the old seal from the valve plug.
Step 3: Install a new seal. If you are using a linear sealing material, wrap it around the cartridge a few turns. If it is a sealing material such as a soft wire, it is only wrapped around the cartridge.
Apply a thin layer of Vaseline oil to the threads of the cartridge and the threads of the packing nut before you reassemble the faucet.