The most common and most likely answer to this crossword clue is the 7 letter word VICTUAL
I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "Supply food" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supply food = victual.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 VICTUAL mean?
VICTUAL noun- Food fit for human consumption.
- (in the plural) Food supplies; provisions.
- Grain of any kind.
- To provide with food; to provision.
- To lay in food supplies.
- To eat.