Exhilarating obsession, crossing stream (9)
I believe the answer is:
thrilling
'exhilarating' is the definition.
('thrill' can be a synonym of 'exhilarate')
'obsession crossing stream' is the wordplay.
'obsession' becomes 'thing' (I've seen this before).
'crossing' is an insertion indicator.
'stream' becomes 'rill' (rill is a kind of stream**).
'thing' placed around 'rill' is 'THRILLING'.
(Other definitions for thrilling that I've seen before include "Extremely exciting" , "Engrossing" , "Sensational" , "Gripping" , "Causing pleasurable excitement" .)