Primarily austere, mostly illiberal, quiet sect (5)
I believe the answer is:
amish
'sect' is the definition.
(Amish sect is an example)
'primarily austere mostly illiberal quiet' is the wordplay.
'primarily' says to take the initial letters.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
The initial letters of 'austere mostly illiberal' is 'ami'.
'ami'+'sh'='AMISH'
(Other definitions for amish that I've seen before include "Relating to a strict US Mennonite sect" , "Relating to a strict American sect" , "Of US Mennonites" , "Mennonite sect members" , "sectarian" .)