expression, ichidan verb
one's term of service expires
Archaic expression used for the end of a fixed term of service, such as an apprenticeship or indentured labor. The cross-reference to 年季 suggests a connection to the concept of a fixed period of service.
See also: 年季
彼は奉公の年が明けて、故郷へ帰った。
His term of service ended, and he returned to his hometown.
年季 refers to a fixed term of service or apprenticeship, while 年が明ける is the archaic verbal expression meaning that term expires.
The expression combines 年 (year/period) with 明ける (to end/expire), literally meaning 'the period opens/ends'. The exact historical derivation is uncertain, but it is associated with the end of a fixed term of service.