In my HS we have a chess team, with optional after-school practises thrice a week (so long as you show up once a week!). We travel to other schools on Tuesdays for matches, bringing along anywhere from 5 to 9 people, dependent on who can come.
Chess without a chess club?
I teach chess at a number of public and private schools in San Francisco. One of the things you can do is to have an informal chess club that meets twice a month. Use any available space (from lunchroom to outside on the playground). You can be in charge of setting up and monitoring the games. Contact your local or regional adult chess club and see if anyone would volunteer to teach a lesson here and there. Many regulars at chess clubs are more than happy to volunteer their time to work with kids. I can walk you through the logistics and provide you with PDF handouts, etc. Just send me a message here at chess.com.
A while back my kid's school had a chess club, but the parent running it gave up. I wouldn't be able to run a regular club, partly due to having an irregular work schedule and partly due to hating to teach. I'm not particularly good at chess either.
I have been considering making the offer of occasionally running a supervised table with a couple of boards at lunchtimes, so long as the school is willing to find someone to teach the moves once a year. I'm quite confident about my ability to stop kids disrupting each other's games, and I'm willing to set up and put away the equipment so the kids can get the whole lunch to play.
Has anyone here seen similar done? How did it work out?