Noble, not having a chance (7)
I believe the answer is:
Here is my best explanation:
'chance' is the definition.
'noble not having a' is the subsidiary indication.
'noble' becomes 'imperial' ('imperial' can be similar in meaning to 'noble').
'not having' suggests deleting specific letters.
'imperial' with 'a' taken out is 'imperil'.
(Other definitions for imperil that I've seen before include "Hazard", "put in danger", "Put at risk", "Put in danger", "Endanger", "Jeopardize", "Threaten, jeopardise" and "Place in danger".)