The most common and most likely answer to this crossword clue is the 7 letter word CHIPPIE
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Buddy explains!

The straight part
We know that "fast-food outlet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fast-food outlet = chippie.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.
What does CHIPPIE mean?
CHIPPIE noun- A fish-and-chip shop.
- A carpenter.
- The youngest member of a team or group, normally someone whose voice has not yet deepened, talking like a chipmunk.
- A potato chip.
- A prostitute or promiscuous woman.
- A chiptune.
- A chipping sparrow.