Is there a relationship between the earthquake in Turkey and the earthquake in Gansu?

No. Earthquakes are caused by pressure accumulation and fault movement in the crust. An earthquake will not directly trigger another earthquake. Gansu and Turkey are located in two different seismic zones, namely Qilian Mountain seismic zone in Hexi Corridor of China and Anatolia seismic zone in Turkey. Although both of them belong to the plate boundary zone, due to the relative movement between plates, the seismic events are independent in time and space, so there is no direct connection.