Competir - lo que nos compete
 

I just heard the following usage of competir. Is this common?

... ahora regresando a lo que nos compete ...

The meaning was something like:

... returning to the topic at hand ...

I was just curious how common this usage is. Thanks! :)

I would say it is quite common, but if I'm not mistaken the infinitive is competer. You also have the noun competencias.
Lo que nos compete is what concerns us, our responsibilities.

I just assumed it was competir, but I guess the 3rd person singular would have been compite then, not compete.

Gemma said right. Competir and competer are different verbs.

It can be added that competer is a defective verb, as you can not conjugate it in all persons. Or, maybe, you can, but it's as uncommon and weird that it's better not to do it.
You can not usually say: Yo competo a mi padre y a mi madre, meaning that you are under responsibility of your parents.
Usually, this verb is only conjugated in the third person, as it's got always an impersonal subject. What compete is always a thing. And, as it usually has got an indirect object, you can think of this verb as those other verbs with OI, like gustar, doler, parecer (when it means to think):

Me compete(n)
Te compete(n)
Le compete(n)
Nos compete(n)
Os compete(n)
Les compete(n)

Muchísimas gracias por la información. :)