Deny rat problem, having left with passion (8)
I believe the answer is:
ardently
'with passion' is the definition.
(I've seen this before)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for ardently that I've seen before include "In a very passionate way" , "Passionately" , "with zeal" , "full of enthusiasm?" , "With passion" .)