Indoctrinate supporter swimming off Hunstanton? (9)
I believe the answer is:
brainwash
'indoctrinate' is the definition.
(brainwashing is a kind of indoctrinating)
'supporter swimming off hunstanton?' is the wordplay.
I cannot really see how this works, but
'supporter' could be 'bra' (a bra gives support to breasts) and 'bra' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for brainwash that I've seen before include "Subject someone to stressful indoctrination" , "Apply pressure" , "Subject to systematic indoctrination" , "Coerce into belief" , "clean mind?" .)