The most common and most likely answer to this crossword clue is the 7 letter word AMPLIFY
I've seen this crossword clue in The Times
A
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More clues leading to the result AMPLIFY
Buddy explains!

The straight part
We know that "to fill out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to fill out = amplify.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 AMPLIFY mean?
AMPLIFY verb- To render larger, more extended, or more intense.
- To enlarge by addition or commenting; to treat copiously by adding particulars, illustrations, etc.; to expand.
- To increase the amplitude of something, especially of an electric current.
- To add content that is not present in the source text to the target text, usually to improve the fluency of the translation.