HfromIL Welcome to FlyerTalk!
I traveled with car seats at least a couple of times per year for about a decade, sometimes with two seats (as a mom alone with two kids), so I fretted about this stuff quite a bit several years ago.
This page is very useful, from the FAA:
https://www.faa.gov/travelers/fly_children##AboutCRS
In the USA, you do have the right to use an approved, correctly sized child restraint for your child under aged 18, but I would carry a printout and have the link handy in case of push back from airline staff. On the other hand, I do not know what rights you have if you fly an international airline or connect in Europe. Hopefully someone else can chime in.
First question:
Is that particular seat important due to some personal needs of your child?
One thing I personally did is switch to a more airline seat friendly car seat just for travel on planes. I had a huge Britax seat installed in my car at home, but I bought an extra, slimmer seat that fit more easily in a plane seat. For me, the extra money was less important than making my life easier when I traveled. Also, uninstalling and reinstalling the car seat was hard, so I spent money to do that less often.
Second question:
Is your child using the ClickTight as a harnessed seat?
Just want to be sure you are aware, booster seats aren't safe or approved to be used on a plane, only harnessed seats. Also, make sure the label is still affixed to your kid's seat stating that it is "Certifed for use in Motor Vehicles and Aircraft." I had that sticker peel off on at least one older car seat, and the airline doesn't have to allow any seat without that label attached.
Third question:
Does your child require the seat in flight, or are you just wanting to be sure you have one in Rome?
For me, as my kids got older, I switched to a lightweight Ride Safer Travel Vest (link below) for flights where I wanted to know I had a safe car seat/restraint for use upon arrival, but after they were comfortable and willing to stay buckled en route. I preferred a hard-shelled, high backed booster at home, but this product made travel much easier with booster-eligible children.
https://saferide4kids.com/
My kids inherited my short stature (and short torso), so one was in a booster up all through middle school until he finally hit his growth spurt. If the booster is just for your child's height, not for special needs, it is helpful to know that the skeleton of an older child (>8 years or so) is typically much more developed, so the risks from using normal seat belts can go down just due to normal growth and development.
Finally, when my kids were in child safety seats, this web site was my go to resource for specialist information. Many posters are technicians who install seats professionally. Maybe they can help if I missed your point entirely.
https://www.car-seat.org/