Subject of note crossing the border (5)
I believe the answer is:
theme
'subject' is the definition.
('theme' can be a synonym of 'subject')
'note crossing the border' is the wordplay.
'note' becomes 'te' (**).
'crossing' is an insertion indicator.
'the border' becomes 'hem' (I've seen this before).
'te' enclosing 'hem' is 'THEME'.
'of' acts as a link.
(Other definitions for theme that I've seen before include "Subject (on which person writes, speaks)" , "Main idea or topic" , "Subject of a talk or piece of writing" , "sort of tune" , "matter for discussion" .)