Acknowledgements from delegations after a day (10)
I believe the answer is:
admissions
'acknowledgements' is the definition.
(admission is a kind of acknowledgement)
'delegations after a day' is the wordplay.
'delegations' becomes 'missions' ('mission' can be a synonym of 'delegation').
'after' is a charade indicator (letters next to each other).
'a day' becomes 'ad' (I've seen this in other clues**).
'missions' after 'ad' is 'ADMISSIONS'.
'from' acts as a link.
(Other definitions for admissions that I've seen before include "Acknowledgments" , "Costs of entering" .)