I suggest you 'engage' the services of a lawyer. [=I suggest you hire a lawyer]
She 'engaged' him 'in' conversation. [=she started a conversation with him]
The book fails to 'engage with' the problems of our time.
(..) Some place in between. They called it automatic art. Let's make this like okay? Engage intellect. Excuse me? I'm Kirk. Your head's the warp drive. Engage intellect. What if Pollock had (..)2014 Ex Machina
(..) What? In between her legs, there's an opening, with a concentration of sensors. You engage them in the right way, creates a pleasure response. So if you wanted to screw her, mechanically speaking, (..)2014 Ex Machina