SharkBite 1/2"x3/8" Compression Angle Stop Brass Plumbing Valve

Not a bad idea to have one of these on hand if you have a toilet shut-off valve you haven't touched in awhile. Old shut-offs tend to leak the second you touch them.

While certainly many exceptions exist most standard residential household plumbing to areas like kitchen sink cabinets, bathroom sink cabinets, toilets, etc is through 1/2" feed lines, be it copper, PEX, etc. from there it typically is reduced to a 3/8" male fitting where you'd connect your 3/8" supply line directly to the fixture. So assuming the pipe below your old shut-off is 1/2" you'd cut that cleanly off (after isolating off course, even if it means shutting the main water supply and opening a faucet below stream to drain residual water), clean the outside of the pipe and debur the inside, set the 1/2" side to proper depth over the 1/2" pipe, close the valve, test the connection by turning the water back on and pressurizing the line, then hook the female 3/8" of your supply line running to the fixture to the 3/8" outlet of this adapter.

Typically if your plumbing source comes out of the wall and your fixture is above that point you use this right angle adapters. If your plumbing comes out of the floor and your fixture is above you'd use a straight connector shut off.

Also it helps to remove the faucet head/aerator anytime you shut water off and turn it back on otherwise they can potentially get clogged by debris.

Edit: Also to save yourself some aggravation you can typically fix a leaking gate valve by tightening the packing nut as they can work themselves loose. this is the nut behind the handle. Usually just an 1/8 of a turn will stop a slow drip but if it doesn't tighten with light force don't overdue it as you can break the valve if you go crazy

$12.45 regular price at Home depot
https://www.homedepot.com/p/Shark.../202270612