Formal term for the head of a cabinet or government; most commonly refers to the prime minister in political contexts.
A new cabinet headed by him was formed.
The election to designate the prime minister was held.
彼は内閣の首班として強いリーダーシップを発揮した。
He demonstrated strong leadership as the head of the cabinet.
The prime minister was nominated as head of government in the Diet.
総理 is a common shortened title for the prime minister used in everyday and media contexts, whereas 首班 is a formal, legalistic term for the same position.
元首 refers to the head of state (e.g. an emperor or president), while 首班 refers specifically to the head of the cabinet/government, so the two are not interchangeable.
Diet nomination of the prime minister
Compound of 首 (head, chief) and 班 (group, squad), literally 'head of a group'. The exact historical derivation is uncertain, but the term has been used in Japanese political vocabulary to refer to the head of a cabinet.