You won't be able to wake up early tommorow if you don't go to bed early
You won't be able to wake up early tommorow if you don't go to bed early =早く寝ないと明日早く起きれなくなるよ
be able to 〜 = 〜が可能である
won't be able to wake upなので「起きれなくなる」となります。
If you don't go to sleep early, you won't be able to get up early tomorrow
If you don't go to sleep early, you won't be able to wake up early tomorrow
If you don't go to sleep early tonight, you won't be able to wake up early tomorrow
早くーEarly
何々しないと、ー If you don't 何々
寝る ー Sleep, go to sleep
明日 ー Tomorrow
起きれない ー Won't be able to get up/wake up (**起きれなくなる** 未来時制です)
似ている文章が：
野菜を食べないと、デザートを食べれない ー If you don't eat your vegetables, you can't have dessert
料金を払わないと、電車に乗れない ー If you don't pay the fare, you can't ride the train
アメリカ合衆国 
オーストラリア 
