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Longman Dictionary of Contemporary English
director-general
noun
EXAMPLES FROM CORPUS
▪ And the director-general has little freedom of manoeuvre.
▪ Baillie and Sherrard resigned in 1932 and Leese became the sole leader of the organization, assuming the title of director-general.
▪ He retired in 1982 in some frustration with the civil service before eventually becoming director-general of the Institute of Directors.
▪ Its master staunchly refused to doff his hat to the director-general.
▪ The director-general should drive, said Swann: the chairman should read the map.
▪ We work for the prison service director-general and negotiate with him.
Wiktionary
director-general

n. the highest chief executive officer within a governmental, statutory, NGO, third sector or non-profit institution. In reference to government, the executive officer below the minister of the department.

Wikipedia
Director-general

Director-general (plural directors-general), or general director, is a title given to the highest executive officer within a governmental, statutory, NGO, third sector or not-for-profit institution. It is commonly used in many countries worldwide, but often with different meanings. Although in most countries it has a business or civil service connotation, in the United States the term "general director" typically refers to the administrative head of an opera house.

Usage examples of "director-general".

And Jacques Necker, the Genevan Director-General of Finance, determined to finance the American war overwhelmingly by loans rather than taxes.

Director-General of the Giza Pyramids, fell upon them, suddenly and unexpectedly, like the proverbial ton of bricks.

CIM Secretary Irwin Schroder and ISA Director-General John Belford exchanged heavy glances while Krantz and Linsay remained silent and expressionless.

President Vaughan Nash and ISA Director-General John Belford were waiting with nervous, unsmiling faces.