Betrothal (10)
I believe the answer is:
<span class="explanation-format__ClueExplanation">'<span class="explanation-format__original">betrothal</span>' is the definition.<br/ ><span class="explanation-format__explanation">(synonyms)</span><br/ ><br/ >This is all the clue.<br/ ></span>
(Other definitions for engagement that I've seen before include "Appointment - conflict" , "pledge between 11 & 6 [WILLIAM & KATE]" , "promise of union" , "get this in the diary?" , "Sort of ring" .)