The most common and most likely answer to this crossword clue is the 11 letter word EXPECTATION
I've seen this crossword clue in The Times
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Buddy explains!

The straight part
We know that "the assumption" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the assumption = expectation.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 EXPECTATION mean?
EXPECTATION noun- The act or state of expecting or looking forward to an event as about to happen.
- That which is expected or looked for.
- The prospect of the future; grounds upon which something excellent is expected to occur; prospect of anything good to come, especially of property or rank.
- The value of any chance (as the prospect of prize or property) which depends upon some contingent event.
- The first moment; the long-run average value of a variable over many independent repetitions of an experiment.
- (colloquial statistics) The arithmetic mean.
- The leaving of a disease principally to the efforts of nature to effect a cure.