Peruse a red construction (4)
I believe the answer is:
read
'peruse' is the definition.
(I've seen this in another clue)
'a red construction' is the wordplay.
'construction' indicates an anagram (answer constructed from certain letters).
'a'+'red'='ared'
'ared' with letters rearranged gives 'READ'.
(Other definitions for read that I've seen before include "Stomach" , "Undertake a course of study" , "Speak" , "Study (subject at university)" , "Interpreted, for example" .)