Don's pressing the snooze button to the left? (3,2)
I believe the answer is:
put on
'don's' is the definition.
(synonyms)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for put on that I've seen before include "Increase as with weight" , "Assume < present" , "Affixed" , "Don; mount (a play)" , "Donned" .)