Obsession followed by the Parisian music maker (5)
I believe the answer is:
bugle
'music maker' is the definition.
(bugle is a kind of musical instrument)
'obsession followed by the parisian' is the wordplay.
'obsession' becomes 'bug'.
'followed by' means one lot of letters go next to another.
'the parisian' becomes 'le' (definite article in French).
'bug'+'le'='BUGLE'
(Other definitions for bugle that I've seen before include "costume ornament?" , "Brass instrument; plant" , "Trumpet-like instrument" , "Mil. trumpet" , "'Last Post' instrument" .)