Curb control, securing backing for cultural pursuits (8)
I believe the answer is:
restrain
'curb' is the definition.
(synonyms)
'control securing backing for cultural pursuits' is the wordplay.
'control' becomes 'rein' (rein is a kind of control).
'securing' means one lot of letters goes inside another.
'backing for' says the letters should be written backwards.
'cultural pursuits' becomes 'arts' (the arts are cultural pursuits).
'arts' written backwards gives 'stra'.
'rein' placed around 'stra' is 'RESTRAIN'.
(Other definitions for restrain that I've seen before include "Keep back" , "Hold back, tether" , "use handcuffs?" , "bottle up" , "Arrest - confine - subdue" .)