He reappeared in public after winning the leadership of the Social Democratic Party.

the 是定冠词，在这里特指"社会民主党的领导权"这一特定职位。 leadership 是名词，由 leader（领导者）加上后缀 -ship（表示状态、职位或关系）构成，意思是"领导地位"或"领导权"。