1. The act of engaging, pledging, enlisting, occupying, or entering into contest.
3. That which engages; engrossing occupation; employment of the attention; obligation by pledge, promise, or contract; an enterprise embarked in; as, his engagements prevented his acceptance of any office. Religion, which is the chief engagement of our league. (Milton)
5. (Science: machinery) The state of being in gear; as, one part of a clutch is brought into engagement with the other part.