Like to get into endless board game pursuits (6)
I believe the answer is:
chases
'pursuits' is the definition.
('chase' can be a synonym of 'pursuit')
'like to get into endless board game' is the wordplay.
'like' becomes 'as'.
'to get into' indicates putting letters inside.
'endless' means to remove the last letter.
'board game' becomes 'chess' (chess is a kind of board game).
'chess' with its final letter taken away is 'ches'.
'as' put inside 'ches' is 'CHASES'.
(Other definitions for chases that I've seen before include "Runs after, pursues" , "Follows in order to catch" , "performs follow-up" , "Pursues or follows" .)