Western isle, and western part of troubled isle (5)
I believe the answer is:
lewis
'western isle' is the definition.
(part of the Western Isles of Scotland)
'western part of troubled isle' is the wordplay.
'western' becomes 'w'.
'part of' means one lot of letters goes inside another (part of the inside).
'troubled' is an anagram indicator.
'isle' is an anagram of 'leis'.
'w' going into 'leis' is 'LEWIS'.
'and' acts as a link.
(Other definitions for lewis that I've seen before include "Hebridean isle" , "Busy" , "Cecil Day ---, Poet Laureate" , "gunman?" , "Charles Dodgson's pen name" .)