Statesmen changed limit on welfare (5,4)
I believe the answer is:
means test
'limit on welfare' is the definition.
(a means test tests eligibility for a benefit)
'statesmen changed' is the wordplay.
'changed' is an anagram indicator.
'statesmen' is an anagram of 'MEANS-TEST'.
(Other definitions for means test that I've seen before include "Inquiry into financial position before providing aid" , "used to give the benefit" , "Check to see if one qualifies for assistance" , "enquiry into funding" , "examination of available funds" .)