The most common and most likely answer to this crossword clue is the 15 letter word VICE-CHANCELLOR
I've seen this crossword clue in The Guardian
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More clues leading to the result VICE-CHANCELLOR
Buddy explains!
The straight part
We know that "Senior administrator/enior administrator/‘s weakness, to risk register being rejected (4-10)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case senior administrator/enior administrator/‘s weakness, to risk register being rejected (4-10) = vice-chancellor.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 VICE-CHANCELLOR mean?
VICE-CHANCELLOR noun- An official holding a rank immediately below that of chancellor.
- A lower judge of chancery.
- In Roman Catholicism, the cardinal whose duty it is to draft and dispatch papal bulls and briefs.