Cover body up in secret niche (5)
I believe the answer is:
inter
'cover' is the definition.
(I've seen this before)
'body up in secret niche' is the wordplay.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'body' says the answer is hidden in the clue (I've seen 'body of' mean this (body can mean the inside of something)).
'retni' is hidden within 'in secret niche'.
'retni' reversed gives 'INTER'.
(Other definitions for inter that I've seen before include "Football Club at home in San Siro" , "Put into the ground" , "Place into grave, tomb" , "Plant" , "Football Club seen in Milan" .)