From https://www.cdc.gov/coronavirus/2019-ncov/vaccines/faq.html :
> If I have already had COVID-19 and recovered, do I still need to get vaccinated with a COVID-19 vaccine?
> Yes, you should be vaccinated regardless of whether you already had COVID-19. That’s because experts do not yet know how long you are protected from getting sick again after recovering from COVID-19. Even if you have already recovered from COVID-19, it is possible—although rare—that you could be infected with the virus that causes COVID-19 again.
Another thing is that, although it hasn't been scientifically studied yet, there are some reports that getting vaccinated has helped some COVID long haulers with their symptoms:
https://www.npr.org/sections/health-shots/2021/03/31/9827994...