The most common and most likely answer to this crossword clue is the 8 letter word PROVIDED
I've seen this crossword clue in The Daily Telegraph
P
R
O
V
I
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D
Buddy explains!
The straight part
We know that "Supplied/on condition" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supplied/on condition = provided.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 PROVIDED mean?
PROVIDED verb- To make a living; earn money for necessities.
- To act to prepare for something.
- To establish as a previous condition; to stipulate.
- To give what is needed or desired, especially basic needs.
- To furnish (with), cause to be present.
- To make possible or attainable.
- (Latinism) To foresee.
- To appoint to an ecclesiastical benefice before it is vacant. See provisor.
- Only if (the stipulation that follows is true).