Leaguer is a noun as well as a transitive verb; just as 'beleaguer' it is derived from the Dutch
leger \; akin to Old German
legar ('bed'). However, as a noun it carries the additional and indeed perhaps pre-eminent meaning of "a military camp".
As a transitive verb it carries the same meaning of 'besiege'.
A tertiary meaning in noun form, derived from 'league' is simply 'member of a league'.
Part of etymology given taken from
www.m-w.com.