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

The straight part
We know that "Supposes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supposes = expects.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 EXPECTS mean?
EXPECTS verb- To predict or believe that something will happen
- To consider obligatory or required.
- To consider reasonably due.
- (continuous aspect only, of a woman or couple) To be pregnant, to consider a baby due.
- To wait for; to await.
- To wait; to stay.