The most common and most likely answer to this crossword clue is the 9 letter word BRAINWASH
I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "convert" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case convert = brainwash.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 BRAINWASH mean?
BRAINWASH noun- A distorting effect upon one's memory, belief, or ideas, as by propaganda.
- To affect one's mind by using extreme mental pressure or any other mind-affecting process. (e.g. hypnosis)
- To take from an electronically controlled machine its stored-up information; to erase a computer's programming. (1960)