At “hair of the dog,” become angry (7)
I believe the answer is:
bristle
'at hair' is the definition.
'bristle' can be an answer for 'hair' (bristle is a kind of hair). I'm not certain of the 'at' bit.
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for bristle that I've seen before include "A short stiff hair, as in beard" , "Get angry" , "Whisker" , "React angrily" , "A stiff hair on chin" .)