Drink shorts with ice? Gin, primarily (4)
I believe the answer is:
swig
'drink' is the definition.
(swig is a kind of drink)
'shorts with ice? gin primarily' is the wordplay.
'primarily' says to take the initial letters.
The first letters of 'shorts with ice gin' is 'SWIG'.
(Other definitions for swig that I've seen before include "Drink deeply" , "(Take) quick drink from bottle" , "Drink quickly from bottle" , "Slug" , "Drink in large draughts" .)