Baggage Limit on Norse

It appears that your bag is 1.5" over the permitted height, so don't be surprised if you have to check it. Many airlines, especially the European ones, are adhering to their restrictions.

Caveats- do you mean Norwegian Airlines?
- my experience was the summer before Covid, so not current, but the carryon rules were the same at that time.
When I checked in (SeaTac) at the Norwegian counter they had a sizer into which the bag had to fit. Mine did, because I couldn't take my Away rolling carryon the same dimensions as yours and also, the weight - it weighed almost 6 pounds when empty.
I ended up using a duffel that weighed 1 and 1/2 pounds and since it wasn't packed totally full with soft sides fit in the sizer. Barely! So the wheels could be a problem for you.
And I had to put some heavy items in my jacket pockets and after months of anxiety about all this, I was at exactly the weight limit.
At one point I just wanted to literally "pack it in" and check the Away bag, but by then it was like a personal challenge.
I am not sure what the checked bag fee is if you pay in advance but likely cheaper than a new suitcase! Or, take a chance but be prepared in case you are asked to check it.

The limit actually is 55cm which technically translates into 21.65”. The airlines round it up to a 22” allowance. We flew Norse Atlantic from LAX with identically-sized 20” Ricardo of Beverly Hills carry-ons that are 21.5” including the wheels. ( $99 on Amazon)! The Norse check-in agent was laser-focused on the weight of the bags but didn’t measure them. Norse does allow you to board with both a personal item with no weight limit AND an additional duty-free shopping bag. If your carry-on is too heavy, you can shift some items to these two that have size limits, but no weight limits.
Be sure to buy a scale so you can weigh your carry-on before your flight back home. Amazon has an “ETEKCITY” scale that weighs just a few ounces for $10.99.
Have a great trip!

Norse airline?? Do you mean Norwegian?

Norwegian Airlines no longer flies across the pond since it became solely a European regional carrier In 2021.
Norse Atlantic Airways operates flights from the U.S. to Europe.