The Yankee great and ESPN broadcaster was recently out with girlfriend Kathryne Padgett in European waters, enjoying the island of Capri and one of its nightclubs called Taverna Anema e Core ... which looks like a swinging hot spot with live music and dancing.

That's exactly what A-Rod and Kat were doing during one of their date nights ... KP, especially, led the charge with a trusty old tambourine that she was shaking and tapping.

Alex got some rattles in too, and eventually ... they shared a kiss. Looks like a pretty sweet, romantic getaway that they're on. And while AR looks quite happy in his new relationship, we can't help but notice a bit of similarity here to what he once shared with J Lo.

Of course, we're talking about Summer 2018, when he and his then-GF were also sailing all over the Amalfi Coast. Granted, that trip was more fitness-geared than this one seems to be.

While things looked pretty magical at the time -- from the outside looking in -- we now know Jen and Alex weren't that great of a fit ... evidenced in her moving on to Ben Affleck, and once again getting engaged. Meanwhile, A-Rod appears quite happy with his new boo.