It's fine as it is. It means, "within the next seven days".
"Your upgrade will take place in the next week, or you can upgrade your account today."
Shouldn't the underlined part be written without "in the?" I think it is wordy, isn’t it? I would write/say, next week/early next week/ last week/this week and so on and so forth.
Thank you,
It's fine as it is. It means, "within the next seven days".
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If it's Tuesday and you say something will happen "next week," then I would not expect it until Monday at the earliest.
"In the next week" means it will happen sometime before the next Tuesday.