Delay set back a big party (4)
I believe the answer is:
gala
'big party' is the definition.
(I've seen this in another clue)
'delay set back a' is the wordplay.
'delay' becomes 'lag' (lag is a kind of delay).
'set back' says the letters should be written backwards.
'lag' reversed gives 'gal'.
'gal'+'a'='GALA'
(Other definitions for gala that I've seen before include "Sports meeting" , "Carnival, celebration" , "Festive celebration" , "Social occasion with special performances" , "Festive event" .)