Shortened notice about game (8)
I believe the answer is:
abridged
'shortened' is the definition.
('abridge' can be a synonym of 'shorten')
'notice about game' is the wordplay.
'notice' becomes 'ad' (both can mean an advertisement).
'about' means one lot of letters goes inside another.
'game' becomes 'bridge' (card game).
'ad' going around 'bridge' is 'ABRIDGED'.
(Other definitions for abridged that I've seen before include "Epitomised" , "Cut short - big adder (anag)" , "Abbreviated, contracted" , "Shorter" , "Shortened as book may be" .)