Terrible anger shown by duke (4)
I believe the answer is:
dire
'terrible' is the definition.
(I know that terrible can be written as dire)
'anger shown by duke' is the wordplay.
'anger' becomes 'ire' (ire is intense rage).
'shown by' means one lot of letters go next to another.
'duke' becomes 'd' (abbreviation).
'ire' put after 'd' is 'DIRE'.
(Other definitions for dire that I've seen before include "'Dreadful, terrible (4)'" , "to speak (13) [FRENCH]" , "Dreadful; grim" , "Very serious indeed" , "Terrible; urgent" .)