Environment Agency upset about MPs heading off for recess (4)
I believe the answer is:
apse
'recess' is the definition.
(apse is a kind of recess)
'environment agency upset about mps heading off' is the wordplay.
'environment agency' becomes 'EA' (abbreviation).
'upset' says the letters should be written in reverse.
'about' means one lot of letters goes inside another.
'heading off' means to remove the first letter.
'ea' backwards is 'ae'.
'mps' with its initial letter taken away is 'ps'.
'ae' enclosing 'ps' is 'APSE'.
'for' is the link.
(Other definitions for apse that I've seen before include "may be seen in church!" , "Rounded end of building" , "where praetor sat" , "Primate holds saint to be a" , "Church's part" .)