When one thinks of the Soviet Union, the last thing on their mind is political freedom. Hearts of Iron IV will make this a bit more historically accurate, especially in portraying the power struggles of the early Stalin era.
As a communist, you will have three main options. One is to stay with the center and keep Stalin as the country leader. That option is self-explanatory and has been covered in the previous dev diary.
The second option you have is a move to the left. If you go down this path, you will end up in a civil war. There was simply no way Stalin would just hand over power to Trotsky or his allies. You have a few things you can do to make life easier for you once the war starts, and to prepare for what comes after.
You can send trusted advisors abroad, in order to keep them safe from Stalin. Relatively safe anyway, stay clear of ice picks. You can tie closer bonds with Smirnov, and his Workers' opposition, who were always close to the left opposition anyway. Additionally, you can convince a few notable Military Officers to side with you. That will strengthen the ties with the military, making your side stronger in the upcoming civil war. For example, Primakov.
Also, Stalin agitated a lot against what he called “wreckers” - organized workers doing planned sabotage - associated with the Trotskyists. Whether historically true or not, you can use that tactic against him and actually organize wrecker squads.
When you feel ready, you complete the “Ignite the Flames” to start the war - unless of course, Stalin’s paranoia has forced your hand already.
Bukharin was one of Stalin’s first allies, and he used him to thwart Kamenev’s plans. Later he got brushed to the side and accused of plotting against Stalin. When the game starts he is out of favor, out of power, but not entirely out of options, so he is also one of our options to choose.
It should be noted though, that the Right opposition will have much lower support within the military than the Left Opposition has - it is after all “Trotsky’s Red Army” - so if push comes to shove you might have to get some help from abroad. For example, you can offer Vladivostok to the Japanese, making them more inclined to support you when the war starts.