At home, see about dog being anxious (8)
I believe the answer is:
insecure
'anxious' is the definition.
(similar in meaning)
'at home see about dog' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'about' is an insertion indicator.
'dog' becomes 'cur' (both can mean a despicable person).
'see' placed around 'cur' is 'secure'.
'in'+'secure'='INSECURE'
'being' acts as a link.
(Other definitions for insecure that I've seen before include "Fearful, unsafe." , "Not adequately protected" , "Loose" , "Not firmly fixed" , "Wavering" .)