To make quiet or put at rest; to pacify or appease; to quell; to calm; as, to allay popular excitement; to allay the tumult of the passions
If you allay someone's fears or doubts, you stop them feeling afraid or doubtful. He did what he could to allay his wife's fears. = calm. allay (sb's) fear/concern/suspicion etc to make someone feel less afraid, worried etc