A spout drip when closed often points toward an internal shutoff component rather than the drain below.
Find the brand or model where possible and record whether the problem is on hot, cold, or both settings. Photos of the faucet and accessible supply arrangement help the provider decide whether parts, full replacement, or a separate valve repair may be needed.
Keep this boundary: A tight handle is not a reliable cure. Extra force can damage the control and make a serviceable part harder to repair.