ADJ

cricket, football, etc.
They want to start a new football league
European, northern, etc.
local, national
Sunday
He played Sunday League cricket for years
premier
major, minor
major league baseball
super
new proposals for a European super league

VERB + LEAGUE

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

LEAGUE + NOUN

champions, leaders
championship, cup, title
club, side
player
game, match
table
cricket, football, etc.

PREP

in a/the ~
The team is now in the Premier League

PHRASES

at the bottom/top of the league, (come) bottom/top of the league, a position in the league
hoping to improve their position in the league

ADJ

big, super, top, world
This move propelled him into the political big league

PHRASES

in a different league
Today's technology is in a different league (= very 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 nearly as good as),
out of sb's league
A house like that is way out of our league (= too expensive for us)