You need to reach level 6 of the wellness skill.
To launch your own nail business, your Sim will need to spend some time building the Wellness skill. You won’t be able to offer nail services until your Sim has level 6 Wellness skill. Once your Sim is at level 6 of the Wellness skill, they can click on a spa chair and select Tend Spa Chair, much the same way your Sims can tend a bar.
While tending a spa chair, your Sim will wait near the chair until nearby Sims wander over to request spa services. Your Sims will automatically offer manicures, pedicures, hand massages, and foot massages while tending a spa chair but if you only want your Sim to do nails or massages, you can disable any services you don’t want your Sim to offer via the spa chair as well.
If your Sim completes the new Self-Care Specialist aspiration, they will earn the Self-Care Expertise reward trait which will allow them to make a lot more money from offering all spa services, including nails! This can be a very lucrative option for your Sims!
https://simscommunity.info/2021/09/07/the-sims-4-spa-day-refresh-all-about-nails/