At the age of 9, Tarkay and his family were sent to the Mathausen Concentration Camp, until Allied liberation freed them a year later. In 1949 his family immigrated to Israel, living in a kibbutz for several years, and by 1951 he had received a scholarship to the Bezalel Art Academy where he studied under the artist Schwartzman. Until his graduation from the Avni Institute of Art in 1956, Tarkay learned a great deal from many famous artists of the time, such as Mokady, Janko, Schtreichman and Stematsky.

Tarkay has achieved recognition as a leading representative of a new generation of figurative artists. The inspiration for his work clearly lies with French Impressionism, and Post-Impressionism, particularly the color sophistication of Matisse and the drawing style of Toulouse-Lautrec, while summing up the characteristics of his model subject without relying on the precise copying of natural forms, or the patient assembling of exact detail. As well as being a painter and watercolorist, Tarkay is a master graphic artist and his rich tapestry of form and color is achieved primarily through the use of the serigraph. In his serigraphs, many colors are laid over one another and used to create texture and transparency.

After exhibiting both in Israel and abroad, he received recognition at the International Art Expo in New York in 1986 and 1987 for works in several forms of media, including oil, acrylic and watercolor. Today, Tarkay is considered one of the most influential artists of the early 21st Century and has inspired dozens of artists throughout the world, with his contemplative depiction of the female figure. Three hardcover books have been written on Tarkay and his art, the most recent, Tarkay, Profile of an Artist was published in 1997.