I moan & moan furiously -- it's an obsession (9)
I believe the answer is:
monomania
'an obsession' is the definition.
(thesaurus)
'i moan moan furiously' is the wordplay.
'furiously' indicates an anagram.
'i'+'moan'+'moan'='imoanmoan'
'imoanmoan' with letters rearranged gives 'MONOMANIA'.
'it's' is the link.
(Other definitions for monomania that I've seen before include "Single-minded passion" , "Unhealthy preoccupation with one thing" , "obsessive single-mindedness" , "Obsession with one thing" .)