In the story I'm plotting, the ruling monarch is overthrown and imprisoned on the basis of colluding with an invading force that's already encroaching the country's boarders. There are letters to corroborate the accusations, however with falsified signatures/handwriting. The monarch escapes and goes into exile.
The country is ruled by the monarch with a council of heads from wealthy families, and in the case the monarch or their spouse is missing, the heir would inherit. However, the current monarch is left without an heir, their spouse presumably dead so the head of the council would reign as a regent of sort.
Side note: During the regent's reign the country becomes a vassal to the invading force to spare lives, resources etc. But not everybody is happy with that.
EDIT: The monarch was away on a meeting of other monarch of the region to discuss the invading nation, prior to the start of the story. The spouse was left to rule but went missing on a hunt for bandits. This turned public opinion from sympathetic to divided because the invading army was approaching and bandits ran amok in the country. The regent would plan to rule forever, and have him family be the next reigning family.
My question is, what are the steps the exiled monarch needs to do to effectively re-establish themselves on the throne, aside from overthrowing the regent directly?