Rector lied about being irritated (5)
I believe the answer is:
riled
'irritated' is the definition.
('rile' can be a synonym of 'irritate')
'rector lied about' is the wordplay.
'rector' becomes 'r'.
'about' indicates an anagram.
'lied' is an anagram of 'iled'.
'r'+'iled'='RILED'
'being' is the link.
(Other definitions for riled that I've seen before include "get angry" , "Nettled" , "Annoyed" , "Cross" , "Made angry" .)