Unconventional lady rent with passion (8)
I believe the answer is:
ardently
'with passion' is the definition.
(I've seen this before)
'unconventional lady rent' is the wordplay.
'unconventional' is an anagram indicator.
'lady'+'rent'='ladyrent'
'ladyrent' is an anagram of 'ARDENTLY'.
(Other definitions for ardently that I've seen before include "With passion" , "Passionately" , "In a very passionate way" , "with zeal" , "full of enthusiasm?" .)