The most common and most likely answer to this crossword clue is the 9 letter word GUARANTEE
I've seen this crossword clue in The Daily Telegraph
G
U
A
R
A
N
T
E
E
More clues leading to the result GUARANTEE
- Ensure aid recipient includes usual application initially
- Protection from age developed with nature
- Promise to get gold back, surrounded by relative support
- Ensure sentry finishes early, with ease, say, to support worker
- Bond‘s nature changed with age
- Promise oddly glum American organised support
- Undertaking to play a great timeless tune
- Protector ultimately failing a new supporter’s pledge
- Agree aunt’s broken promise
- Eager aunt has broken promise
Buddy explains!

The straight part
We know that "Promise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case promise = guarantee.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 GUARANTEE mean?
GUARANTEE noun- Anything that assures a certain outcome.
- A legal assurance of something, e.g. a security for the fulfillment of an obligation.
- More specifically, a written declaration that a certain product will be fit for a purpose and work correctly; a warranty
- The person to whom a guarantee is made.
- A person who gives such a guarantee; a guarantor.
- To give an assurance that something will be done right.
- To assume or take responsibility for a debt or other obligation.
- To make something certain.