Extremely sensitive singer consuming a fish (3,4)
I believe the answer is:
sea bass
'fish' is the definition.
(I know that sea bass is a type of food fish)
'extremely sensitive singer consuming a' is the wordplay.
'extremely' means to remove the middle letters (letters on the extremes of the word are used).
'sensitive' becomes 'sore' (as in a sore wound).
'singer' becomes 'bass' (bass is a kind of singer).
'consuming' is an insertion indicator.
'sore' with its centre removed is 'se'.
'se'+'bass'='sebass'
'sebass' going around 'a' is 'SEA-BASS'.
(Other definitions for sea bass that I've seen before include "Marine food fish" , "one showing off plenty of scales" , "Edible marine fish" , "Saltwater fish" .)