Engrossed in getting into gear? (7)

I believe the answer is:

engaged

I'm a little stuck... Click here to teach me more about this clue!

'engrossed in' is the definition.
(thesaurus)

I don't understand how the rest of the clue works.

(Other definitions for engaged that I've seen before include "Promised in marriage" , "Busy - fiancee" , "Held" , "Formally committed to marriage" , "Plighted; hired" .)

I've seen this clue in the Evening Standard.

Want a hint initially instead of a full solution? Install my app