1 [transitive] engage something (formal) to succeed in attracting and keeping somebody's attention and interestIt is a movie that engages both the mind and the eye.Their pleas failed to engage any sympathy.
2 [transitive] engage somebody (as something)| engage something| engage somebody to do something (formal) to employ somebody to do a particular jobHe is currently engaged as a consultant.We will have to engage the services of a translator.3 [intransitive] engage (with something/somebody) to become involved with and try to understand something/somebodyShe has the ability to engage with young minds.4 [transitive, intransitive] engage (somebody) (formal) to begin fighting with somebodyto engage the enemy5 [intransitive, transitive] when a part of a machine engages, or when you engage it, it fits together with another part of the machine and the machine begins to workThe cogwheels are not engaging.engage with something One cogwheel engages with the next.engage something Engage the clutch before selecting a gear.Opposite
disengagePhrasal verbs

ɪnˈɡeɪdʒ
ɪnˈɡeɪdʒ