Innocent person I put in cooler sent up (4)
I believe the answer is:
naif
'innocent person' is the definition.
(I've seen this in another clue)
'i put in cooler sent up' is the wordplay.
'put in' indicates putting letters inside.
'cooler' becomes 'fan' (something which cools).
'sent up' says the letters should be written in reverse.
'i' going within 'fan' is 'fian'.
'fian' reversed gives 'NAIF'.
(Other definitions for naif that I've seen before include "Innocent" , "Unworldly" , "wide-eyed" , "Unsophisticated" , "somewhat ingenuous" .)