In 1944, Kleshchev became first secretary of the Pinsk Oblast Committee of the Communist Party. Between 1946 and 1948, he served in the same position for Polotsk Oblast. From 1948 to 1953, Kleshchev was Chairman of the Council of Ministers of the Byelorussian SSR. For the next two years, he studied at the courses of the CPSU Central Committee, then was first secretary of the Kokshetau Oblast Party Committee in Kazakhstan until 1960. Kleshchev retired in 1961 and lived in Moscow, where he died on 13 December 1968. He was buried in the Novodevichy Cemetery.
