The most common and most likely answer to this crossword clue is the 5 plus 3 letter word SNACK BAR
I've seen this crossword clue in Financial Times
S
N
A
C
K
B
A
R
More clues leading to the result SNACK BAR
- Diner's bag filled with new piece of chocolate
- Fire consuming nothing at first, except this eatery
- Pub on fire, engulfing end of kitchen where food’s served
- Cab ranks supply eatery
- It may offer a sandwich course
- Refreshment at pub or cafe
- Fast food ban here? Never!
- Cab ranks offering quick fare here?
- Fast food outlet‘s flapjack?
- Barack’s worried about new cafe!
Buddy explains!

The straight part
We know that "eatery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eatery = snack bar.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.