With 4K on a GoPro, you're looking at roughly 400-600 MB per minute, depending on which resolution and bitrate you're using. That means an hour of filming eats up between 24-36 GB. So theoretically, with 128 GB you can film for 3-5 hours straight before the card fills up. For a whole week of vacation, that's obviously not enough if you're out shooting several hours every day.
I'd recommend getting at least one or two extra cards. A second 128GB or better yet a 256GB or 512GB card makes sense. They're not expensive anymore, and then you won't constantly have the problem of the card filling up during your trip. Don't forget to format the cards beforehand and test them briefly to make sure they work fine - sometimes you get weird compatibility issues.
Here's a practical tip: If you have access to a laptop or external hard drive during your vacation, you can back up your footage occasionally and then delete and reuse the cards. That saves you from having to haul around tons of storage. Just make sure when you're formatting that you're using an SD card that's specifically approved for 4K recording - not all cards can handle that high write speed.