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' says to put letters next to each other.
'cold' becomes 'C' (eg on taps).
'rage' becomes 'ire' (ire is intense rage).
'c' next to 'ire' is 'cire'.
'cire' backwards 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" .)