The spell Find Steed allows a Paladin to "summon a spirit that assumes the form of an unusually intelligent, strong, and loyal steed, creating a long-lasting bond with it." The spell text describes what happens when a creature itself is reduced to 0 hit points (it disappears) but not what happens to it if the Paladin dies. The spell does not require concentration so it will not end because of that. Since the spirit is bound to the Paladin, it could make sense for the bound to break after the Paladin's death.
Is there any other advice that the rules provide or would this fall under the DM's discretion?