Clearly, Q is neither a hockey player nor a chess player. So, he must be a football player and thus cannot be a lady. T is a husband (not a lady) and so must be a chess player. Hence, R must be a hockey player, and therefore she must be a lady and T's wife. So, the information can be summarised as follows :
P -- unmarried lady, does not participate in games.
Q -- brother of R, football player.
R -- hockey player, T's wife.
S -- unmarried lady, does not participate in games.
T -- husband of R, chess player

So, T is the chess player.