Alcalde-presidente

An alcalde-presidente is an alcalde who also functions as president of a higher administrative level.
Cases include:

colonial San Juan on Puerto Rico, 1879–1902; the last one succeeded himself as first 'normal' alcalde
in Spain:
*Mayor-President of Ceuta, the head of government of Ceuta, an autonomous city
*Mayor-President of Melilla, the head of government of Melilla, autonomous city

As Singapore is a city-state, its president can be thought of a mayor who also functions as a president of a higher administrative level; however, the President of Singapore, though not entirely ceremonial, is not the city-state's chief executive. The prime minister is.