I won't write much as I'm on mobile right now. Essentially after Stalin's death in March 1953, a joint leadership of Malenkov, Beria, Khrushchev, Molotov and Bulganin took shape, who had different ambitions for the USSR, but at first meant to uphold a joint leadership. Essentially, Khrushchev was able to strengthen his own position by leading the charge against Beria, who was from the start alienated from the rest as leader of the NKVD, and with the support of army leaders such as Zhukov (who had suffered in prestige in the aftermath of the great patriotic war by Stalin instrumentalising the NKVD) had him arrested in June of 1953. At that time Malenkov still seemed the most potent successor to Stalin's legacy, but Khrushchev was able to secure the position of first secretary of the CPSU in September, allowing him to appoint his own supporters in key positions. This would prove critical, as Malenkov announced his New Course programme that same October to expand the production of consumer goods and improve relations to the West, whereas Khrushchev further emphasised heavy industry and agriculture (for now). By sheer party political pressures, Malenkov eventually resigned his position as chairman of the council of ministers in February 1955. His successor Bulganin would prove to be an ally of Khrushchev until he eventually took up the position himself in 1958.

Source: A History of Twentieth-Century Russia - Robert Service