Terrible anger shown by daughter (4)
I believe the answer is:
dire
'terrible' is the definition.
('dire' can be a synonym of 'terrible')
'anger shown by daughter' is the wordplay.
'anger' becomes 'ire' ('ire' can be a synonym of 'anger'**).
'shown by' means one lot of letters go next to another.
'daughter' becomes 'd'.
'ire' after 'd' is 'DIRE'.
(Other definitions for dire that I've seen before include "Desperate, horrendous" , "Catastrophic" , "Extremely serious or urgent" , "Really dreadful - ride on" , "'Dreadful, terrible (4)'" .)