Big time Native American (5)
I believe the answer is:
osage
'native american' is the definition.
(I've seen this before)
'big time' is the wordplay.
'big' becomes 'os'.
'time' becomes 'age' (an age is a period of time).
'os'+'age'='OSAGE'
(Other definitions for osage that I've seen before include "Member of the Native American people, once occupying the Missouri valley" , "Native Americans from Missouri - age so (anag)" , "Language" , "Indian people" , "Amerindian" .)