1 proceed or move or act (against), take (legal) action or bring suit or prefer charges (against); summon(s), charge, accuse:
He threatened to sue. They are suing him for the injuries they sustained.
2 petition, beg, plead, entreat, pray, request, solicit, apply, beseech, implore, supplicate:
After five years of constant warfare, the country is suing for peace.