Can I insert rests?

[pdxdjazz]

No can do, at least, not yet. NC (no chord) silences the two instrument tracks but not the drums.
The feature tacet (rests/breaks) has been talked about. It'll happen when/if it happens.

Another option to try would be to bring up the player control screen and slide the drums to OFF in real-time using the mixer feature. You could also record the track to another device or perhaps midi-export, fix it and play it fom the other device.

Remember, the player feature was added to the app as a "practice" tool. That some are using it in performance is a reflection of the great work of the developers!
)BOB