Ban of coaster is ludicrous (9)
I believe the answer is:
ostracise
'ban' is the definition.
('ban'->'ostracize' is in my internal thesaurus and 'ize'->'ise')
'coaster is ludicrous' is the wordplay.
'ludicrous' is an anagram indicator.
'coaster'+'is'='coasteris'
'coasteris' with letters rearranged gives 'OSTRACISE'.
'of' is the link.
(Other definitions for ostracise that I've seen before include "Exclude from a group or society" , "Cast out, send to Coventry" , "Blackball, send to Coventry" , "Shun, exclude" , "exile" .)