Pay for part of score that's relatively unimportant (8)
I believe the answer is:
footnote
'that's relatively unimportant' is the definition.
'pay for part of score' is the wordplay.
'pay for' becomes 'foot' (as in to foot the bill).
'part of score' becomes 'note' (part of a musical score).
'foot'+'note'='FOOTNOTE'
(Other definitions for footnote that I've seen before include "Minor reference" , "It's not very important" , "Text at page end" , "Text explanation" , "Comment at bottom of page" .)