A tidally locked moon still rotates, it just rotates in resonance with it's orbit around the planet. So as long as the day isn't really long (10+ days), you should still get a 3 cell atmospheric structure. At least in theory.

The other major atmospheric drivers are the temperature differential between the night/dark sides and between the equator/poles. Those would still apply as well.

That said, I'm sure it's more complicated than that. This is definitely something I'll try to look into further...