Tommy, in an effort to maintain clowning's positive roots, invite dancers to weekly performance battles.

How should the sentence above be rewritten to correct the subject-verb agreement error?

Here we can observe that the verb used doesn't reflect the correct tense to express when this action took/is taking/will take place. There are many tenses where you could choose from, depending of the time of action:

Tenses: Simple, Progressive, Perfect, Perfect progressive

Times: Past, Present, and Future

Imagine all the combinations!

The simplest example we could make is if this action is a routine that happens continuously, the action verb (invite) is changed to simple present for the third person of singular (invites):

Tommy, in an effort to maintain clowning's positive roots, invites dancers to weekly performance battles.