Ambition about to be admitted by mother (5)
I believe the answer is:
dream
'ambition' is the definition.
('dream' can be a synonym of 'ambition')
'about to be admitted by mother' is the wordplay.
'about' becomes 're' (regarding).
'to be admitted by' indicates putting letters inside.
'mother' becomes 'dam' (female parent of an animal).
're' placed into 'dam' is 'DREAM'.
(Other definitions for dream that I've seen before include "Cherished hope; fantasy" , "Aspiration" , "Cherished hope or ideal" , "Fantastic but vain hope" , "It's experienced during sleep" .)