Got rid of old American Cruz? (6)
I believe the answer is:
ousted
'got rid of' is the definition.
(to oust is to remove from power)
'old american cruz?' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'american' becomes 'us' (abbreviation for United States).
'cruz?' becomes 'Ted' (US politician Ted Cruz).
'o'+'us'+'ted'='OUSTED'
(Other definitions for ousted that I've seen before include "Driven out" , "Put forcibly out of office" , "Expelled from office or power" , "Removed from office (6)" , "Forcibly ejected from office or position" .)