Piggy is middle character of three in game (6)
I believe the answer is:
porker
'piggy' is the definition.
(both can mean a pig)
'of three in game' is the wordplay.
'of three' becomes 'r' (I can't justify this - if you can you should believe this answer much more).
'in' means one lot of letters goes inside another.
'game' becomes 'poker' (poker game is a kind of game).
'r' going within 'poker' is 'PORKER'.
'is middle character' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
(Other definitions for porker that I've seen before include "Little swine" , "A pig raised for food and named for its meat" , "Piglet," , "Young fattened pig" , "Hog" .)