The most common and most likely answer to this crossword clue is the 8 letter word REBUFFED
I've seen this crossword clue in The Daily Telegraph
R
E
B
U
F
F
E
D
More clues leading to the result REBUFFED
Buddy explains!

The straight part
We know that "rejected" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rejected = rebuffed.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 REBUFFED mean?
REBUFFED verb- To refuse; to offer sudden or harsh resistance; to turn down or shut out.
- To buff again.