Doing time? That's cool (2,2,4)
I believe the answer is:
up to date
'cool' is the definition.
(up to date can mean cool or modern)
'doing time?' is the wordplay.
'doing' becomes 'upto' (as in 'what are you up to?').
'time?' becomes 'date' (date is a kind of time).
'upto'+'date'='UP-TO-DATE'
'that's' acts as a link.
(Other definitions for up to date that I've seen before include "absolutely fresh" , "in fashion" , "That's for girlfriend to decide" , "Thoroughly modern" , "Following modern trends" .)