A girl gets on around mid-morning (5)
I believe the answer is:
agnes
'a girl' is the definition.
'gets on around mid-morning' is the wordplay.
'gets on' becomes 'ages' (get on can mean to get older).
'around' indicates putting letters inside.
'mid' says to take the centre.
The middle letter of 'morning' is 'n'.
'ages' enclosing 'n' is 'AGNES'.
(Other definitions for agnes that I've seen before include "lass" , "Tube for cables" , "Miss Grey" , "Scandinavian singer" , "St --' Eve, poem by Lord Tennyson" .)