The most common and most likely answer to this crossword clue is the 13 plus 3 letter word MEDITERRANEAN SEA
I've seen this crossword clue in The Times
M
E
D
I
T
E
R
R
A
N
E
A
N
S
E
A
Buddy explains!
The straight part
We know that "Name eater associated originally with sardine?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case name eater associated originally with sardine? = mediterranean sea.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.