The handle must be removed to allow access to the retainer clip, then the cartridge pulls out. You may need a cartridge puller if the faucet is old.
No conversion, it would need to be replaced with a single handle faucet.
Change the faucet, either one will mount on the sink.
The handle. The handle attaches to the stem. The stem is part of the valve. Single handle or quarter turn faucets, the stem is in a cartridge. That should cover it. The handle on a faucet does not have a special name, it is just a handle. ________________________________ It's called a spigot.
The o rings inside the cartridge have become either faulty, worn or perished. You need to replace the cartridge for you to solve this problem.
On the single lever handle just unscrew it.
They either have a cup and spring that stops the water or you change a cartridge. Also a couple of O rings to seal around the handle. Shut the water off, take the handle off and there is a nut holding the stem in place. Remove the nut and pull straight up on the stem. It is either a cartridge or there will be a black rubber cup in the hole with a spring under it. Single handle has two of them. Replace both the cup and spring and reassemble. If a cartridge, replace it making sure it goes in the same way the old one was sitting. There should be a small notch in the faucet and a matching tab on the cartridge
if it is a single lever faucet the cartridge needs to be replaced. check the supply valve under the sink first,
Turn the water off to the faucet. Remove the handle. The top of the faucet should unscrew to get to the ball valve. Replace the valve and gaskets then reassemble the faucet.
A single handle uses the same 3 holes as the double handle
Moen part #1920 and a brand new Moen single handle faucet
Look under the handle for a small ALLEN SCREW (hex head). Loosen it and slide the handle off.
The Belvedere 622TC faucet is a single handle " pull up" faucet that is used in the commercial hair industry. Very common in your basic beauty salons at there hair washing sinks.