Stimulate some backing for clear-up session (4)
I believe the answer is:
spur
'stimulate' is the definition.
(I've seen this before)
'some backing for clear-up session' is the wordplay.
'backing for' is a reversal indicator.
'some' indicates a hidden word (some of the parts of the word are used).
'rups' is hidden in the letters of 'clear up session'.
'rups' backwards is 'SPUR'.
(Other definitions for spur that I've seen before include "Incite to action" , "footballer?" , "Incentive; branch line" , "Projection on cock's leg" , "Cowboy's goading instrument" .)