The most common and most likely answer to this crossword clue is the 9 plus 4 letter word ELLESMERE PORT
I've seen this crossword clue in The Times
E
L
L
E
S
M
E
R
E
P
O
R
T
Buddy explains!
The straight part
We know that "Cheshire town" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cheshire town = ellesmere port.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.