Here, there's success for a slimmed down father (6)
I believe the answer is:
hither
'here' is the definition.
(I know that here can be written as hither)
'success for a slimmed down father' is the wordplay.
I cannot really understand how this works, but
'success' could be 'hit' (a hit is a commercial success) and 'hit' is found within the answer.
The remaining letters 'her' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'there's' is the link.
Can you help me to learn more?
(Other definitions for hither that I've seen before include "Towards this place - not yonder" , "In this direction" , "Hit her, being towards this place" , "all over the place - 13a,25a,16d,15d" , "Formally, towards this place" .)