Bring up commendation, but not initially (5)
I believe the answer is:
raise
'bring up' is the definition.
(raising is a kind of bringing up)
'commendation but not initially' is the wordplay.
'commendation' becomes 'praise' (praise is a kind of commendation).
'but not initially' means to remove the first letter.
'praise' with its first letter removed is 'RAISE'.
(Other definitions for raise that I've seen before include "Heighten" , "Wage increase" , "Bring up a salary increase" , "Gather" , "Put up" .)