The Hayase clan used to be a proud clan during the era of shinobi clans, long before the formation of the shinobi villages.
During the era of the shinobi clans, the Hayase clan used to reign and conquer other clans in the land of Water. Eventually, they got overconfident and entered the land of Fire to try and expand their territory. After four months, they were defeated by the Uchiha clan, with their clan leader being killed by Madara Uchiha. Deprived of their strongest fighter, they retreated back to the land of Water
Eventually, they formed an alliance with the Uzumaki clan ond was part of the founding of Uzushiogakure. When the village was destoryed, they scattered and later reformed as a wandering clan.