Going up like top children's specialist (6)
I believe the answer is:
ascent
'going up' is the definition.
(ascending means going up)
'like top children's specialist' is the wordplay.
'like' becomes 'as'.
'top' suggests taking the first letters.
'specialist' becomes 'ent' (Ear, Nose and Throat specialist).
The initial letter of 'childrens' is 'c'.
'as'+'c'+'ent'='ASCENT'
(Other definitions for ascent that I've seen before include "progress" , "Upward journey" , "advancement" , "Upwards motion" , "Going up" .)