Indoctrinate supporter’s husband touring in western area (9)
I believe the answer is:
brainwash
'indoctrinate' is the definition.
(brainwashing is a kind of indoctrinating)
'supporter's husband touring in western area' is the wordplay.
'supporter's' becomes 'bras'.
'husband' becomes 'h'.
'touring' means one lot of letters goes inside another (touring can mean going round).
'western' becomes 'w'.
'area' becomes 'a' (maths abbreviation).
'bras'+'h'='brash'
'in'+'w'+'a'='inwa'
'brash' placed around 'inwa' is 'BRAINWASH'.
(Other definitions for brainwash that I've seen before include "Condition" , "Subject to systematic indoctrination" , "clean mind?" , "Coerce into belief" , "Apply pressure" .)