I have entrance exams next year so I can't go but I'll go the year after!
I can't go next year because I have entrance exams but I'll go the next after!
「受験」→「Entrance exams」
「来年」→「Next year」
「The year after」→「その次の年」
「いける」→「Can go」
まとめて言いますと、
「I have entrance exams next year so I can't go but I'll go the year after!」
「I can't go next year because I have entrance exams but I'll go the next after!」
になります。
どちらでも使えます。