While Visenya Targaryen rode Vhagar in the past, Princess Laena Velaryon (Nanna Blondell) owns her in the "House of the Dragon" timeline. We even see her flying alongside her husband, Prince Daemon Targaryen (Matt Smith) as they head back to Pentos.
Unfortunately, Laena goes through a traumatic birth in episode six that puts both her and her child at risk, and she forces Vhagar to end her suffering by incinerating her with that all-important phrase: "Dracarys."