Cryptic crossword clue
University, rather unorthodox, that’s used by a peer 7

The most common and most likely answer to this crossword clue is the 7 letter word URETHRA

I've seen this crossword clue in The Guardian
U
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Buddy explains!

The straight part
We know that "that’s used by a peer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s used by a peer = urethra.
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 URETHRA mean?

URETHRA noun
  1. The tube through which urine exits the body and, in penises, through which semen is ejaculated.

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