Deity has time to gasp (4)
I believe the answer is:
pant
'to gasp' is the definition.
(synonyms)
'deity has time' is the wordplay.
'deity' becomes 'pan' (Pan is an example).
'has' means one lot of letters go next to another.
'time' becomes 't' (abbreviation).
'pan'+'t'='PANT'
(Other definitions for pant that I've seen before include "Sound out of breath" , "Gasp for breath (like a hot dog?)" , "Breathe noisily after running" , "Breath noisily from exertion" , "Breathe heavily" .)