Card game includes right pig (6)
I believe the answer is:
porker
'pig' is the definition.
(porker is a kind of pig)
'card game includes right' is the wordplay.
'card game' becomes 'poker' (poker is a kind of card game).
'includes' is an insertion indicator.
'right' becomes 'r' (common abbreviation).
'poker' going around 'r' is 'PORKER'.
(Other definitions for porker that I've seen before include "Little swine" , "Young fattened pig" , "A pig raised for food and named for its meat" , "Hog" , "Piglet," .)