The most common and most likely answer to this crossword clue is the 8 letter word ABNEGATE
I've seen this crossword clue in The Daily Telegraph
A
B
N
E
G
A
T
E
More clues leading to the result ABNEGATE
- Refuse to drop off around noon, for example
- Deny Blunt’s smuggled back dope
- Refuse in bag eaten – disgusting!
- Deny scandal of sailor from Tyneside?
- Refuse to accept sailor, one hiding head by entrance
- Deny oneself information offered up during decline
- Deny Blunt’s smuggled dope from the East
- Deny being negative in a fit of temper
- Renounce retired General in decline
Buddy explains!

The straight part
We know that "Deny oneself" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deny oneself = abnegate.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 ABNEGATE mean?
ABNEGATE verb- To deny (oneself something); to renounce or give up (a right, a power, a claim, a privilege, a convenience).
- To relinquish; to surrender; to abjure.