The most common and most likely answer to this crossword clue is the 9 letter word POSTULATE
I've seen this crossword clue in Financial Times
P
O
S
T
U
L
A
T
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Buddy explains!

The straight part
We know that "Suppose" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suppose = postulate.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 POSTULATE mean?
POSTULATE noun- Something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument. Sometimes distinguished from axioms as being relevant to a particular science or context, rather than universally true, and following from other axioms rather than being an absolute assumption.
- A fundamental element; a basic principle.
- An axiom.
- A requirement; a prerequisite.
- To assume as a truthful or accurate premise or axiom, especially as a basis of an argument.
- To appoint or request one's appointment to an ecclesiastical office.
- To request, demand or claim for oneself.
- Postulated.