Native from one quarter runs to here when thrown out (10)
I believe the answer is:
southerner
'native from one quarter' is the definition.
(someone from the south)
'runs to here when thrown out' is the wordplay.
'when thrown out' indicates anagramming the letters.
'runs'+'to'+'here'='runstohere'
'runstohere' is an anagram of 'SOUTHERNER'.
(Other definitions for southerner that I've seen before include "Alabaman" , "One from lower down the country" .)