Finish off anxiety to get some fish (7)
I believe the answer is:
pomfret
'some fish' is the definition.
(pomfret is a kind of fish)
'finish off anxiety' is the wordplay.
'finish off' becomes 'pom' (I can't justify this - if you can you should give a lot more credence to this answer).
'anxiety' becomes 'fret' (I've seen this before).
'pom'+'fret'='POMFRET'
'to get' is the link.
Can you help me to learn more?
(Other definitions for pomfret that I've seen before include "sort of cake" , "cake, Yorkshire style" , "Round flat liquorice sweet - Asian food fish" .)