There isn't a way from within the apps to enter Live touraments, if that is what you are asking.
There is a Tournament link in the New Game screen but that takes you to the Correspondence tourneys web page (embedded into the app) where you can join one if you want.
I have heard, though have never tried it, that you can join a Live tourney on the website and then play the games on the app. I have never done it and don't know if that is really a supported solution or one that might stop working in the future or not.
Can I enter tournaments via the chess app for iOS? Thank you