v.
     - attract or involve (someone's interest or attention).
- employ or hire. ▸enter into a contract to do. 
- 
(engage in/with)
 participate or become involved in.
- (with reference to a part of a machine or engine) move into position so as to come into operation.
- enter into combat with. ▸(of fencers or swordsmen) bring (weapons) together preparatory to fighting. 
Etymology
  ME (orig. in the sense ‘pawn or pledge something’): from Fr. engager, ult. from the base of gage1.