We recently lost one of our resident Pickering experts due to a, well, disagreement with site management, but I'll try my best. The good news is that the Pickering V-15 has some in-house siblings. It's the same cartridge as a Stanton 500, and both of these also exist in P-mount versions. So in total you have four families of styli that will all fit.
The bad news is they're all long out of production. What's left of Stanton/Pickering is owned by Gibson guitars, which itself is in financial trouble. Aftermarket suppliers have a hard time making good replacements.
A good starting point is The Voice of Music, known around here as TVOM. No affiliation other than being a satisfied customer.
https://www.thevoiceofmusic.com/catalog/phono_needles.asp
Look for Pfanstiehl numbers 604, 605, 820 and 826. You'll see only a few remaining originals, mostly in the higher tracking force range originally intended for jukeboxes etc., and none of them cheap.
To get going and find out if you even like the sound, there's a seller on ebay named felo3000 who's been offering Colombian-made TEI brand styli for years. About $12 shipped. I haven't tried one myself but they are said to be excellent for the price, and made exactly like the originals. They are however simple conicals, even though some of the listings say otherwise.
I used a Pickering DE stylus on mine for quite a while. That's one of the P-mount versions, which means nominally 1.25g tracking force and thus best used with a "light" tonearm. Hard to find now and usually priced out of proportion to what it is.
Finally, some similar sounding model numbers to
avoid: Pickering XV-15, Pickering V-15 Micro IV, Shure V-15. Those are all incompatible.