Take him to participate in Scholastic Chess Tournaments and let him test the waters. It helps if you can get his entire chess club from school to participate, because then you at least win a team prize and the kids are not disappointed if they don't do well. You may need to do the organizing to the extent that you want to organize the school club participation - email list and contact address of parents, list of scholastic competitions, car pools, snacks, group pictures, write up in school newsletter, t-shirts, yearbook pictures etc to keep the momentum going
The chess clubs in schools, rec centers, daycares, PTAs are usually run by vendors like Silver Knights or independent coaches. They are not at all inclined your kid to participate in the real scholastic competions so going to the local, state and national tournaments is on you. Also, the people in the know who have their own kids, teams, schools, clubs in the play will misguide you so do your own research
My favorites websites for tournaments -
MD Chess.
https://www.mdchess.com/
US Chess Federation
https://new.uschess.org/
Virginia Chess Federation
https://www.vachess.org/
The beauty of Chess is that no one can stop your kid from participating and increasing in their ranking if they are good.
Don't be a lazy parent. Don't stick to play online games and tournaments only and think that you are doing what you can do. Chess require studying, thinking, practicing, nerves, brains, stamina, patience, accuracy in calculation etc.