Two jobs in one word.

As a noun: a person who supports Stalin's kind of rule — one party, no disagreement allowed, the state in control of everything, fear as a tool. Historically, a member or supporter of the Soviet Communist Party under Stalin, or a follower of that line in a communist party somewhere else. Almost nobody today calls themselves this; it is a label other people apply, usually as an accusation, and it was often thrown between rival communist groups (Stalinists against Trotskyists, for example).

As an adjective: describing something as belonging to that period or having that character — a Stalinist purge, Stalinist architecture (those heavy, grand, decorated buildings from the era), Stalinist policies. In loose everyday use it just means harshly controlling and intolerant of disagreement: 'a Stalinist management style'. That loose use is common in newspapers and in arguments, and it is a strong word — strong enough that people use it to shut a conversation down rather than to describe anything precisely.