She had pop award reduced (4)
I believe the answer is:
gran
'she had pop' is the definition.
(a gran could be the mother of one's father or pop)
'award reduced' is the wordplay.
'award' becomes 'grant' (synonyms).
'reduced' means to remove the last letter.
'grant' with its last letter taken away is 'GRAN'.
(Other definitions for gran that I've seen before include "elderly relative" , "Relation" , "nan" , "Older relative" , "Mum's mum" .)