Dole from Kansas has a reputation for helping the less prosperous in society (7,5)
I believe the answer is:
welfare state
'dole from kansas has a reputation' is the definition.
I can't tell whether this definition defines the answer.
'helping the less prosperous in society' is the wordplay.
'helping' becomes 'welfare' (welfare is a kind of helping).
'the less prosperous in society' becomes 'state' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'welfare'+'state'='WELFARE STATE'
'for' acts as a link.
Can you help me to learn more?
(Another definition for welfare state that I've seen is " free in our country?".)