Game men with desire, heading off into dances (7)
I believe the answer is:
Here is my best explanation:
'game men' is the definition.
'desire heading off into dances' is the subsidiary indication.
'desire heading off' becomes 'ish' (I can't justify this - if you can you should believe this answer much more).
'into' means one lot of letters goes inside another.
'dances' becomes 'bops' (bopping is a kind of dancing).
'ish' placed within 'bops' is 'bishops'.
'with' is the link.
(Other definitions for bishops that I've seen before include "Prelates", "Chess pieces" and "Men".)