To enter into (an activity), to participate (construed with in).
To entangle.
That engages the attention; engrossing, interesting; enthralling. Example: I found the first of the Harry Potter books a very engaging read.
Charming; attractive, especially of a manner or behaviour. Example: Beauty, of course, and a bright, engaging personality — or at least the ability to fake one — are prerequisites for entering the Miss World competition.
All clues having "ENGAGING"
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You can find a list of possible crossword clues for ENGAGING below.