Leave, terribly angry about having been exposed (8)
I believe the answer is:
revealed
'exposed' is the definition.
('reveal' can be a synonym of 'expose')
'leave terribly angry about' is the wordplay.
'terribly' indicates anagramming the letters.
'angry' becomes 'red' (someone may go red when angry).
'about' is an insertion indicator.
'leave' anagrammed gives 'veale'.
'veale' going inside 'red' is 'REVEALED'.
'having been' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for revealed that I've seen before include "Made known to others" , "Shown" , "Discovered" , "Exposed" , "Made clear and visible" .)