Longman Dictionary of Contemporary English - engage

~ v formal 1 to attract someone and keep their interest  (The new toy didn't engage the child's interest for long.) 2 to arrange to employ someone  (engage sb to do sth)  (His father engaged a private tutor to improve his maths.) 3 to make one part fit into another part of a machine  (She engaged the clutch and the car moved forwards.)  (The wheel engages with the cog and turns it.)  (- opposite disengage (2)) 4 to begin to fight with an enemy  (The two armies engaged at dawn.) engage in formal phr v 1 to take part or become involved in an activity  (a politician engaged in various business activities) 2 engage sb in conversation to start talking to someone and involve them in a conversation.