Can bring my clarinet as my ‘extra personal item’ on the plane?
That’s fine, and it’s fairly common, because it is in the same category as a purse or camera bag (but you should still try to consolidate everything into the smallest possible number of items). Here’s an additional good reminder: if while in Europe you purchase souvenirs that “must” be hand-carried (because they’re fragile, sentimental, easily-lost, etc.), make sure you have a plan for the return trip. A carry-on, clarinet and a bag of souvenirs might be a difficult load.