Radio observations of tidal disruption events (TDEs) - when a star is tidally disrupted by a supermassive black hole (SMBH) - provide a unique laboratory for studying outflows in the vicinity of SMBHs and their connection to accretion onto the SMBH. Radio emission has been detected in only a handful of TDEs so far. Here, we report the detection of delayed radio flares from an optically-discovered TDE. Our prompt radio observations of the TDE ASASSN-15oi showed no radio emission until the detection of a flare six months later, followed by a second and brighter flare, years later. We find that the standard scenario, in which an outflow is launched briefly after the stellar disruption, is unable to explain the combined temporal and spectral properties of the delayed flare. We suggest that the flare is due to the delayed ejection of an outflow, perhaps following a transition in accretion states. Our discovery motivates observations of TDEs at various timescales and highlights a need for new models.