1The next part of a story or work that was left off; the next installment or sequel.
そのドラマの続きが気になって、次の回が待ちきれない。
I'm dying to know what happens next in that drama; I can't wait for the next episode.
話の続きを聞かせてもらえますか。
Could you tell me the rest of the story?
前回の続きから授業を始めましょう。
Let's start the lesson from where we left off last time.
この小説には続きがあり、来月発売されるそうだ。
This novel has a sequel, which is apparently coming out next month.
2The way a piece of writing or story flows and connects; its pacing or smoothness of development.
この文章は続きが不自然で、読みにくい。
The flow of this piece of writing feels unnatural and is hard to read.
台本の場面の続きをもう少し滑らかにしたい。
I want to make the transitions between scenes in the script a bit smoother.
3An uninterrupted succession or run of something; attached after a noun, as in 雨続き ("a spell of rainy days").
雨続きの毎日で、洗濯物が乾かない。
It's been raining day after day, so the laundry won't dry.
忙しさが続きで、ゆっくり休む時間もない。
It's been one busy stretch after another, so I don't even have time to rest.
好天続きのおかげで稲刈りが順調に進んでいる。
Thanks to the stretch of good weather, the rice harvest is going smoothly.