Final answer:
Hugh Gaitskell was the leader of the Labour Party who aimed to get it re-elected by showcasing unity and sensible policies before the 1959 general election.
Step-by-step explanation:
The individual described as the Labour Party leader aiming to get re-elected by proving the party's unity and sensibility of policies before the general election of 1959 is Hugh Gaitskell. It is during Gaitskell's leadership that the Labour Party worked to present itself as a cohesive and responsible option to the British electorate, which is essential for gaining political power through democratic elections. The period saw the Labour Party striving to demonstrate its capabilities through unified efforts and pragmatic policy proposals.