Game men with desire, heading off into dances (7)
I believe the answer is:
bishops
'game men' is the definition.
(chess pieces)
'desire heading off into dances' is the wordplay.
'desire' becomes 'wish' (wishing is a kind of desiring).
'heading off' means to remove the first letter.
'into' indicates putting letters inside.
'dances' becomes 'bops' (bopping is a kind of dancing).
'wish' with its initial letter removed is 'ish'.
'ish' placed within 'bops' is 'BISHOPS'.
'with' is the link.
(Other definitions for bishops that I've seen before include "Prelates" , "Chess pieces" , "Men" .)