The most common and most likely answer to this crossword clue is the 4 letter word FESS
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More clues leading to the result FESS
Buddy explains!

The straight part
We know that "Admit to/a band across the middle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case admit to/a band across the middle = fess.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 FESS mean?
FESS verb- To confess; to admit.
- A horizontal band across the middle of the shield.
- (British dialect) Proud; conceited.
- (British dialect) Lively; active; strong.
- (British dialect) Of animals, bad-tempered, fierce.