Put cover around area (4)
I believe the answer is:
laid
'put' is the definition.
(I've seen this before)
'cover around area' is the wordplay.
'cover' becomes 'lid' (lid is a kind of cover**).
'around' means one lot of letters goes inside another.
'area' becomes 'a' (maths abbreviation).
'lid' going around 'a' is 'LAID'.
(Other definitions for laid that I've seen before include "spread on a surface" , "Produced eggs" , "Doze" , "Placed horizontally on a surface" , "Prepared (a trap)" .)