Replace Water Shutoff Valve Stem with Repair Kit
Easiest fix  - You have leaking packing (the seal around the valve stem) since it leaks only when open.


Tighten the packing nut - hold the valve body still with one wrench so it does not try to twist the pipes while using another wrench to tighten the nut between the valve body and the valve handle (the "packing nut")
If that does not fix it, shut off the water further back in your system and remove the packing nut (same process but loosen) - remove any old packing, apply new packing (hardware store plumbing section should stock it - teflon string, more or less, these days) then reassemble and tighten as in 1.
You may need to take the valve stem out to repack. You can replace the sealing washer if needed which might make it easier to get shut off, depending on the condition of the sealing washer at present. This is rather less drastic than "a valve stem kit" that might or might not actually fit your particular valve.


If you do replace, get a 1/4 turn shutoff valve. They are far less prone to leaking or failing to operate after years of sitting open, as shutoff valves do.