The effect of γ-irradiation on the relaxor properties of the TlInS2<V> compound have been studied. It is established that in this compound the Vogel-Fulcher temperature (Tf) shifts towards the low temperatures, and the Burns temperature (Td) moves towards the high temperatures. As a result, the temperature range for the existence of a relaxor state extends by ~ 40 K. The presence of hopping conduction is established and the parameters characterizing this mechanism are determined.