The most common and most likely answer to this crossword clue is the 5 plus 1 letter word VETO –
I've seen this crossword clue in The Daily Telegraph
V
E
T
O
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“
Buddy explains!

The straight part
We know that "Rejection" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rejection = veto –.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 VETO – mean?
VETO – noun- A political right to disapprove of (and thereby stop) the process of a decision, a law etc.
- An invocation of that right.
- An authoritative prohibition or negative; a forbidding; an interdiction.
- To use a veto against.