The offense of vexatiously persisting in inciting lawsuits and quarrels WordNet 3.0 & Open English WordNet

Barratry is a legal term that, at common law, described a criminal offense committed by people who are overly officious in instigating or encouraging prosecution of groundless litigation, or who bring repeated or persistent acts of litigation for the purposes of profit or harassment. Wikipedia

Litigation for the purpose of harassment or profit Wikipedia Disambiguation

Furtherance of groundless litigation or litigation for the purpose of harassment Wikidata

The act of persistently instigating lawsuits, often groundless ones. Wiktionary