The following year; the next year. Often used in narratives or reports to indicate the year after a referenced event. Can often be replaced by 翌年 or 来年 depending on context.
優勝した翌試合のあくる年、彼はプロ契約を結んだ。
The year after the match he won, he signed a professional contract.
あくる年には景気が少し回復したと報告された。
It was reported that the economy recovered somewhat in the following year.
卒業のあくる年に海外留学する予定だ。
I plan to study abroad the year after graduation.