expression, godan verb (-ku)
enter government service; take up a public office
Formal, somewhat literary expression for assuming a government post or becoming a public official.
彼は大学卒業後、官に就いた。
After graduating from university, he entered government service.
就任する is a more general term for assuming any office or post, while 官に就く specifically refers to entering government or public service.
Fixed expression composed of 官 (government official/post) + に + 就く (to take up a position). The exact historical origin is uncertain, but it follows a classical pattern for assuming an official role.