In 1949 he and his family immigrated to Israel and were sent to a transit camp for new arrivals at Beer Ya'akov. Their next two years were spent in a Kibbutz.
In 1951, Tarkay received a scholarship to the Bezalel Art Academy in Jerusalem, where he studied for a year before having to leave due to difficult financial circumstances at home. In order to continue his scholarship, he was allowed to study under the artist Schwartzman until his mobilization to the Israeli army. After returning to the familiar environment of Tel Aviv, Tarkay enrolled in the Avni Institute of Art, which he graduated in 1956. His teachers there were Mokady, Janko, Schtreichman and Sematsky.
Tarkay has since exhibited extensively both in Israel and abroad, and his works can be found in many public and private collections.