The most common and most likely answer to this crossword clue is the 9 letter word DUNSTABLE
I've seen this crossword clue in The Times
D
U
N
S
T
A
B
L
E
More clues leading to the result DUNSTABLE
- Out to lunch after day in market town
- Demand to settle firm in industrial town
- Luton's neighbour close to Bedford — not sure
- Brownish-grey horse, and where it may be kept in a Bedfordshire town?
- Little daughter getting wobbly in town
- Bedfordshire town located on the right, round the bend
- Daughter lacking balance in Bedfordshire town
Buddy explains!

The straight part
We know that "market town" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case market town = dunstable.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.