The part leading to terrible noise out of court (7)
I believe the answer is:
section
'the part' is the definition.
(section is a kind of part)
'terrible noise out of court' is the wordplay.
'terrible' is an anagram indicator.
'out of' is an insertion indicator.
'court' becomes 'ct'.
'noise' with letters rearranged gives 'seion'.
'seion' enclosing 'ct' is 'SECTION'.
'leading to' is the link.
(Other definitions for section that I've seen before include "Distinct part" , "branch" , "Segment" , "surgical procedure" , "Divide; part" .)