Neat playing in May's wedding ceremony (9)
I believe the answer is:
matrimony
'wedding ceremony' is the definition.
(I've seen this before)
'neat playing in may's' is the wordplay.
'neat' becomes 'trim' (synonyms).
'playing' becomes 'on' (on can mean playing or performing).
'in' is an insertion indicator.
'trim'+'on'='trimon'
'trimon' placed into 'may' is 'MATRIMONY'.
(Other definitions for matrimony that I've seen before include "State of being married" , "Nuptials" , "wedding ceremony" , "The state of wedlock" .)