The phrase "international prominence" refers to being well-known and highly respected on a global scale. It means achieving a prominent status or recognition that extends beyond national borders. Full definition
The move is part of the events long term ambitions to gain international prominence. (northlandsquare.com)
There, she became a leading light in the town's famous artistic community during its post-war period of international prominence. (bbc.co.uk)
This was a common approach: explaining a work's significance and emphasizing how its acquisition would increase the museum's international prominence while sprinkling in a few jokes. (artnews.com)