Chap upset by cold rage (4)
I believe the answer is:
eric
'chap' is the definition.
'upset by cold rage' is the wordplay.
'upset' says the letters should be written backwards.
'by' is a charade indicator (letters next to each other).
'cold' becomes 'C' (eg on taps).
'rage' becomes 'ire' (ire is anger).
'c'+'ire' is 'cire'.
'cire' back-to-front is 'ERIC'.
(Other definitions for eric that I've seen before include "..... the Red was Norwegian 10th Century exployer" , "Rice turned for the boy" , "-- Sykes; -- Idle" , "Blair, perhaps" , "- Morecambe, comic" .)