major league 
noun North American
The highest-ranking league in a particular professional sport, especially baseball: [as modifier]: major-league players...
- Like most of us, my dreams of setting foot on a major-league baseball field died a painful, inglorious death in youth.
- Did you realize the Oakland A's have three players in their starting lineup who are the sons of former major-league baseball players?
- Palmeiro is no longer a major-league caliber ballplayer.
Derivatives
major-leaguer
- Abreu is an established major-leaguer and a future star who is sure to make an impact
- He was a star in Japan, and he has all the tools, but who knows if he can produce as a major-leaguer?
- Even if I wasn't working to become a major-leaguer, I just wanted to play.