en·gage / enˈgāj/ • v. 1. [tr.] occupy, attract, or involve (someone's interest or attention): he tried to engage Sutton's attention. ∎  (engage someone in) cause someone to become involved in (a conversation or discussion). ∎  arrange to employ or hire (someone): he was engaged as a trainee copywriter. ∎  pledge or enter into a contract to do something: he engaged to pay them $10,000 against a bond. ∎ dated reserve (accommodations, a place, etc.) in advance: he had engaged a small sailboat.2. [intr.] (engage in) participate or become involved in: organizations engage in a variety of activities (be engaged in) some are actively engaged in crime. ∎  (engage with) establish a meaningful contact or connection with: the teams needed to engage with local communities. ∎  (of a part of a machine or engine) move into position so as to come into operation: the clutch will not engage. ∎  [tr.] cause (a part of a machine or engine) to do this. ∎  [tr.] enter into conflict or combat with (an adversary).

ENGAGE

To become involved with, do, or take part in something.

To be engaged in something, such as a type of employment, implies a continuity of action. It is used in reference to an occupation or anything in which an individual habitually participates.

A person can also be engaged to do a particular activity by contract or other agreement.

When two people become engaged to marry, they are bound together by an agreement or promise to marry one another.

engage pledge or secure by a pledge XV; persuade, win over XVII; employ, occupy; bring or come into conflict; hire for employment XVIII; attract, charm. — (O)F. engager; see EN-1, GAGE1.
So engagement XVII.