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.
(..) - Do you know where he is? - Hey, hey. We got a man down! - Come on, let's go. Are you okay? What happened? Break surveillance and engage. Continuing sweep... - Insuricare. - Oh, hello. This is Helen Parr. Bob Parr is my husband. I was wondering if you could give me (..)2004 The Incredibles
(..) Violet! "Simon J. Paladino, longtime advocate of superhero rights, is missing"? - Gazerbeam. - Bob! It's time to engage. Do something! Don't just stand there! - I need you to intervene! - You want me to intervene? Okay. I'm intervening! (..)2004 The Incredibles