Minshu no Teki (2017)

Both involve an unusual and seemingly unqualified political candidate who surprises everyone and succeeds because of their genuine and down-to-earth understanding of everyday citizens and their concerns. Both also discuss real issues in Japanese politics and society.

Into the Ring is based on this J-drama
Both have female leads who fall into politics due to their circumstances
Both characters come from lesser backgrounds and have to move their way up using their street smarts and strong character
Both discuss how politics work in their respective countries
Only difference is there's not much emphasis placed on romance than Into the Ring