Anywhere from 200 to 2000 hours, depending on the cartridge design and stylus profile.
I’ve written about this elsewhere, but the increased contact area of line contact gems leads to lower contact pressure, less friction, lower wear and better sound. The best line-contact types can last 2000 hours or more, but line-contact styli are more expensive to manufacture, so there is a price to pay. By contrast, cheap spherical/conical and elliptical styli generally only last for 200 – 300 hours. So you could get 5 – 10 times more life from a really good cartridge/stylus, which can more than offset their increased cost.
Other factors must be considered, including poorly designed, low-quality turntables and older types with excessive tracking force. These can experience more rapid stylus wear, and cause accelerated record wear. Even the best cartridges, tracked at lower than recommended tracking forces, can experience accelerated record and stylus wear.
It’s important to replace a stylus before it becomes worn or it will destroy your records. For moving magnet cartridges, this is fairly straightforward, as long as a quality replacement can be sourced. I often supply quality Japanese JICO and Nagaoka styli for older cartridges.
For moving coil cartridges, stylus replacement involves bonding a new diamond to the existing cantilever or installing a new cantilever and diamond. Several vendors provide this service.