Sea cook’s story verbally identifying worker in precious metal (11)
I believe the answer is:
silversmith
'worker in precious metal' is the definition.
'sea cook's story verbally' is the wordplay.
'sea cook's' becomes 'silvers' (Long John Silver, cook in Treasure Island).
'story' becomes 'myth' (myth is a kind of story).
'verbally' shows a homophone (sound like).
'myth' is a homophone of 'mith'.
'silvers'+'mith'='SILVERSMITH'
'identifying' is the link.
(Other definitions for silversmith that I've seen before include "Craftsman" , "artisan" , "Argentine worker" , "Metalworker" , "Fine metal worker" .)