The most common and most likely answer to this crossword clue is the 9 letter word ACCESSION
I've seen this crossword clue in The Times
A
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The straight part
We know that "acquisition" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case acquisition = accession.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 ACCESSION mean?
ACCESSION noun- A coming to; the act of acceding and becoming joined
- Increase by something added; that which is added; augmentation from without.
- A mode of acquiring property, by which the owner of a corporeal substance which receives an addition by growth, or by labor, has a right to the part or thing added, or the improvement (provided the thing is not changed into a different species).
- The act by which one power becomes party to engagements already in force between other powers.
- The act of coming to or reaching a throne, an office, or dignity.
- The invasion, approach, or commencement of a disease; a fit or paroxysm.
- Agreement.
- Access; admittance.
- To make a record of (additions to a collection).