Perhaps fin or tail of whiting are broken at the end (5)
I believe the answer is:
organ
'perhaps fin' is the definition.
(fish fins are organs)
'or tail of whiting are broken at the end' is the wordplay.
'tail of' says to take the final letters.
'are' becomes 'a' (short for 'are', historical unit of measurement).
'at the end' indicates one should take the final letters.
The final letter of 'whiting' is 'g'.
The last letter of 'broken' is 'n'.
'or'+'g'+'a'+'n'='ORGAN'
(Other definitions for organ that I've seen before include "Air-powered instrument" , "Wurlitzer, for example" , "Church instrument - heart, perhaps" , "Wind and keyboard instrument" , "music producer" .)