Old comedian's second fish factory Gina organised (5,8)
I believe the answer is:
spike milligan
'old comedian's' is the definition.
'second fish factory gina organised' is the wordplay.
'second' becomes 's' (common abbreviation).
'fish' becomes 'pike' (pike is a kind of fish**).
'factory' becomes 'mill' ('mill' can be a synonym of 'factory').
'organised' indicates an anagram.
'gina' with letters rearranged gives 'igan'.
's'+'pike'+'mill'+'igan'='SPIKE MILLIGAN'
(Other definitions for spike milligan that I've seen before include "zany personality" , "Author of Silly Verse for Kids" , "Comedian and author" , "Comedian - alien milks pig (anag)" , "Goon who wrote "Silly Verse For Kids"" .)