One on horseback arresting a pirate, say (6)
I believe the answer is:
raider
'pirate say' is the definition.
(I know that buccaneer is a type of raider)
'one on horseback arresting a' is the wordplay.
'one on horseback' becomes 'rider' (someone riding a horse).
'arresting' means one lot of letters goes inside another.
'rider' placed around 'a' is 'RAIDER'.
(Other definitions for raider that I've seen before include "Pillager, plunderer" , "Viking" , "One plundering" , "Marauder" , "Invader" .)