• 官庁かんちょう — government office
• 警官けいかん — police officer
• 外交官がいこうかん — diplomat
• 官職かんしょく — official post, position
• 官僚かんりょう — bureaucrat

The radical 宀 (うかんむり) suggests a roof or house. 官 originally represented a group gathered under a roof, implying governance or officialdom. This evolved into the concept of an appointed authority or administrator in various systems of government.

彼かれは 外交官がいこうかんとして 働はたらいています。
He works as a diplomat.

官庁かんちょうで 手続てつづきを行おこないました。
I completed the procedure at a government office.

🎧 The on-yomi カン is the only reading in modern use and appears in almost all compound words. There is no common kun-yomi. It is heavily used in public, political, and administrative vocabulary.