Create a special period price list with a Start date on the day your new prices begin and no End date. From that date, it replaces the standard price list on the courts you choose, with no end. Edits to a standard price list apply immediately, so don't use them to schedule a change.
Steps
Go to Settings → Price Lists → Special Period Price Lists.
Click Add price list (or Create new price list if you have none).
Enter a name, for example "Prices from 1 January".
Set the Start date. Leave End date blank.
In Prices and Opening days and times, enter your new price and the hours players can book.
In Courts, tick the courts it applies to, or switch on All courts.
Click Create.
Open the new list and click Add new price variant for each off-peak price or other variant you need. Add cohort prices to each variant with ⋮ → Edit.
Check before the start date
Every hour you want open has a price. The special list replaces the standard list, so unpriced hours can't be booked.
You've added all your off-peak variants and cohort prices to the special list. Duplicate isn't available, so enter them again.
Every court is ticked.
Good to know
Bookings made before the start date keep their old price, even if they're played after it.
If you add a court later, tick it on this special list too. Otherwise the new court uses the old standard prices.
Want a temporary price instead? Set both a start date and an end date. The standard list applies again after the end date.