en·gage 
/ɪnˈgeɪʤ/ verb
en·gag·es; en·gaged; en·gag·ing /ɪnˈgeɪʤ/ verb 1 [+ obj] formal : to hire (someone) to perform a particular service
▪ He was engaged as a tutor. : to pay for (help, services, etc.) ▪ I suggest you engage the services of a lawyer. [=I suggest you hire a lawyer] 2 [+ obj] : to get and keep (someone's attention, interest, etc.)
▪ He sure can engage an audience. ▪ The story engaged my interest. 3 : to start fighting against (an opponent) [+ obj] ▪ The troops prepared to engage the enemy. [no obj] (formal) ▪ The troops prepared to engage with the enemy. — opposite disengage 4 : to move (a mechanism or part of a machine) so that it fits into another part [+ obj] ▪ He engaged the clutch and drove away. [no obj] ▪ As I released the clutch, the gears engaged. — opposite disengage
▪ He was engaged as a tutor. : to pay for (help, services, etc.) ▪ I suggest you engage the services of a lawyer. [=I suggest you hire a lawyer]
▪ He sure can engage an audience. ▪ The story engaged my interest.
engage in [phrasal verb] 1 engage in (something) : to do (something)
▪ At college she engaged in various sports. ▪ We don't engage in that sort of behavior. 2 engage (someone) in (something) : to cause (someone) to take part in (something)
▪ She engaged him in conversation. [=she started a conversation with him]
▪ At college she engaged in various sports. ▪ We don't engage in that sort of behavior.
▪ She engaged him in conversation. [=she started a conversation with him]
engage with [phrasal verb]
engage with (someone or something) formal : to give serious attention to (someone or something)
▪ The book fails to engage with the problems of our time. : to become involved with (someone or something) ▪ a teacher who will not engage with the students
▪ The book fails to engage with the problems of our time. : to become involved with (someone or something) ▪ a teacher who will not engage with the students
