Terrible anger, being at a dead end (4)
I believe the answer is:
dire
'terrible' is the definition.
('dire' can be a synonym of 'terrible')
'anger being at a dead end' is the wordplay.
'anger' becomes 'ire' ('ire' can be a synonym of 'anger'**).
'being at' says to put letters next to each other (I've seen this in other clues).
'end' indicates one should take the final letters.
The final letter of 'dead' is 'd'.
'ire' put after 'd' is 'DIRE'.
(Other definitions for dire that I've seen before include "Terrible display" , "to speak (13) [FRENCH]" , "Catastrophic" , "Portentous" , "Dreadful; grim" .)