Vhagar is first ridden during the Targaryen conquest, when she is the dragon of Queen Visenya, the sister-wife of Aegon I. Many years later, after going riderless after Visenya's death, Vhagar is claimed by Laena Velaryon, the first wife of Prince Daemon Targaryen. Following Laena's death, Vhagar becomes the dragon of Aemond Targaryen, the son of Viserys I by his second wife, thus fighting in the civil war on the side of Aegon II. Vhagar is in the battle that kills the dragon Meleys but suffers only minor injuries. Ultimately, Vhagar is killed in the enormous Battle Above the Gods Eye, where she fatally fight Daemon and his dragon Caraxes.
We can assume that "House of the Dragon" will depict some of these great battles, so keep an eye out for Vhagar!