Collocations for engage - verb

actively, directly
Our contributors are actively engaging with tradition.

fully, seriously
constructively, effectively, successfully
critically, emotionally, intellectually, politically
The party is attempting to engage young voters politically.

fail to, refuse to

with
We acknowledge the need to engage directly with these problems.

actively
people who actively engage in shaping the world they live in

constructively
They constructively engage critics in debates.

openly
regularly, routinely (esp. AmE)
The army was regularly engaged in combat.

attempt to, seek to, try to
He tried to engage me in conversation.

be eager to, be willing to
be reluctant to, be unwilling to

Engage is used with these nouns as the subject:
clutch

Engage is used with these nouns as the object:
audience, clutch, consultant, enemy, first, gear, imagination, mind, staff, student, sympathy, target, tutor, worker