The most common and most likely answer to this crossword clue is the 10 letter word SUSTAINING
I've seen this crossword clue in The Guardian
S
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Buddy explains!

The straight part
We know that "holding up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case holding up = sustaining.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 SUSTAINING mean?
SUSTAINING verb- To maintain, or keep in existence.
- To provide for or nourish.
- To encourage or sanction (something).
- To experience or suffer (an injury, etc.).
- To confirm, prove, or corroborate; to uphold.
- To keep from falling; to bear; to uphold; to support.
- To aid, comfort, or relieve; to vindicate.
- The process by which something is sustained or upheld.
- That sustains, supports or provides sustenance.