Extreme characters in Westminster touch down in African state, once (9)
I believe the answer is:
swaziland
'african state once' is the definition.
(former name of Eswatini)
'extreme characters in westminster touch down' is the wordplay.
'extreme characters' becomes 'az' (I've seen this in other clues).
'in' means one lot of letters goes inside another.
'westminster' becomes 'swi' (resembles SW1, London postcode).
'touch down' becomes 'land'.
'az' going within 'swi' is 'swazi'.
'swazi'+'land'='SWAZILAND'
'in' acts as a link.
(Other definitions for swaziland that I've seen before include "Southern African kingdom, capital Mbabane" , "Southern African country, capital Mbabane" , "territory that's in Africa" , "African state" , "South African region" .)