Born in Riga in the Russian Empire (today in Latvia), Keshet attended a Hebrew high school in his home city.

He joined the Betar youth movement and helped establish the Estonian branch in 1932.

He also became a member of Betar's enlistment battalion and of the central committee of the National Labour Federation in Eretz-Israel, on which he served between 1939 and 1942.

He was a member of the Public Council for Soviet Jewry and was on the Controller Committee of Housing Ministry.

In 1969 he was elected to the Knesset on the Gahal list (an alliance of Herut and the Liberal Party) and became a Deputy Speaker.