Generally speaking, parrots do not need their beaks trims. If they do, then diet and health need to be looked at - unless the overgrowth is due to an injury. (rarely caused by lack of chewing - but it is a possibility)
My Charlie has to have his beak dremeled due to an injury (I say it's his fault!). He picked on a blind ruby macaw and got the short end of the stick... this happened when he was 12 years old. He's 24 this year.
Other than giving him smaller pellets (I've had larger pellets, chomped in half, fly into my eye from a few feet away!), he doesn't receive any special care other than getting beak trims. He eats and drinks fine on his own.