Giving a guarantee, which is auspicious (9)
I believe the answer is:
Here is my best explanation:
'auspicious' is the definition.
(similar in meaning)
'giving a guarantee which is' is the wordplay.
I cannot really see how this works, but
'is' is found in the answer.
This explanation may well be incorrect...
(Other definitions for promising that I've seen before include "Giving one's word", "Favourable -- hopeful", "Encouraging" and "Showing great potential".)