Starts to pull hair out, being in abject fear (6)
I believe the answer is:
phobia
'fear' is the definition.
(phobia is a kind of anxiety disorder)
'starts to pull hair out being in abject' is the wordplay.
'starts to' says to take the initial letters.
The initial letters of 'pull hair out being in abject' is 'PHOBIA'.
(Other definitions for phobia that I've seen before include "Irrational fear (of thing)" , "A lasting abnormal fear of something" , "An irrational fear or dislike" , "15 [EUROPHOBE] 's problem" , "Great fear of something" .)