Republic disperses beatniks pursuing sawn-off gun (10)
I believe the answer is:
uzbekistan
'republic' is the definition.
'disperses beatniks pursuing sawn-off gun' is the wordplay.
'disperses' is an anagram indicator.
'pursuing' means one lot of letters go next to another.
'sawn-off' means to remove the last letter.
'gun' becomes 'uzi' (military weapon).
'uzi' with its last letter removed is 'uz'.
'beatniks' is an anagram of 'bekistan'.
'bekistan' after 'uz' is 'UZBEKISTAN'.
(Other definitions for uzbekistan that I've seen before include "Central Asian country, capital Tashkent" , "Asian republic" .)