Attachment to a department study raising some dirt (8)
I believe the answer is:
addendum
'attachment' is the definition.
(thesaurus)
'a department study raising some dirt' is the wordplay.
'department' becomes 'd' (abbreviation eg in MOD Ministry of Defence).
'study' becomes 'den' (term for a study or office).
'raising' is a reversal indicator (in a down clue, letters go up).
'some dirt' becomes 'mud' (mud is a kind of dirt).
'mud' reversed gives 'dum'.
'a'+'d'+'den'+'dum'='ADDENDUM'
'to' is the link.
(Other definitions for addendum that I've seen before include "Piece added on" , "Item appended to book" , "Dud ad-men dealt with in end of book" , "Something attached to the end, say of book" , "Extra item added at end of book" .)