At a broken date, he gets angry (6)
I believe the answer is:
heated
'angry' is the definition.
(I've seen this before)
'at a broken date he' is the wordplay.
'at' means one lot of letters go next to another.
'a broken' indicates an anagram.
'date' is an anagram of 'ated'.
'ated' after 'he' is 'HEATED'.
'gets' is the link.
(Other definitions for heated that I've seen before include "Of discussion, angry and hostile" , "Angry, getting warm" , "Furious" , "Brief extract" , "Fired-up" .)