Mum is ahead of time, but not as close (7)
I believe the answer is:
miserly
'close' is the definition.
(I've seen this in another clue)
'mum is ahead of time but not as' is the wordplay.
'mum' becomes 'ma' (ma can mean mother).
'ahead of time' becomes 'early' (synonyms).
'but not' is a deletion indicator.
'as' becomes 'AA' (two letter A's).
'ma'+'is'+'early'='maisearly'
'maisearly' with 'aa' taken out is 'MISERLY'.
(Other definitions for miserly that I've seen before include "Penny-pinching" , "Near" , "Mean with money" , "Paltry" , "Like Scrooge" .)