Aspiration about to be suppressed by mother (5)
I believe the answer is:
dream
'aspiration' is the definition.
('dream' can be a synonym of 'aspiration')
'about to be suppressed by mother' is the wordplay.
'about' becomes 're' (regarding).
'to be suppressed by' indicates putting letters inside (I've seen this in other clues).
'mother' becomes 'dam' (female parent of an animal).
're' inserted into 'dam' is 'DREAM'.
(Other definitions for dream that I've seen before include "Cherished hope; reverie" , "Fantasy; imagine" , "Part of sleep" , "Cherished hope; fantasy" , "Think vaguely" .)