Tyrant's place on the outskirts of Dundee (6)
I believe the answer is:
despot
'tyrant's' is the definition.
('despot' can be a synonym of 'tyrant')
'place on the outskirts of dundee' is the wordplay.
'place' becomes 'spot' ('spot' can be a synonym of 'place'**).
'on' says to put letters next to each other.
'the outskirts of dundee' becomes 'de' (first and last letters of 'Dundee').
'spot' after 'de' is 'DESPOT'.
(Other definitions for despot that I've seen before include "Posted (anag)" , "Cruel absolute ruler" , "One exploiting rule" , "Autocrat" , "Tyrant, dictator" .)