Collocations for league - noun

basketball, cricket, football, soccer, etc.
They want to start a new football league.

sports (esp. AmE)
the standard for professional sports leagues in this country

local, national
summer (esp. AmE), winter (esp. AmE)
Premier (in the UK)
major, minor
major league baseball

big
Hopefully he'll get called up to the big leagues soon.

junior, youth
Little League (in the US)
a baseball field with a Little League game going on

professional
the first women's professional athletic league in the US

fantasy
players for a team in a fantasy league

create, form, set up, start
enter, join
The team joined the Northern League last year.

dominate, lead
The Yankees dominated the league in 1998.

win

champions, leaders
championship (esp. BrE), cup (BrE), title
club, side (BrE), team
player
game, match (esp. BrE)
final
table (BrE)
The team slipped to the foot of the Northern League table.
school league tables (= showing how well schools are performing)

record
He set a league record for the longest touchdown run.

baseball, cricket, football, etc.

in a/the league
The team is now in the Premier League.

at the bottom of the league, at the top of the league
come bottom of the league, come top of the league
a position in the league
They're hoping to improve their position in the league.

big, super, top, world (BrE)
This move propelled him into the political big league. (BrE)
This move propelled him into the political big leagues. (AmE)

in a different league
Today's technology is in a different league (= much better).

in a league of your own
As a painter he is in a league of his own (= much better than others).

not in the same league (as … ) (= not as good as)
out of sb's league
A house like that is way out of our league (= too expensive for us).