What happens next is entirely dependent on the rest of the Allied strategy. By round 6 USA/UK should have done something that will warrant Axis attention.
If the UK held on to the Middle East, then you can use ICs in Egypt, Iraq, or Persia to dribble up units to help the Russians hold the south. Usually you might be doing this by vectoring them over to the Ukraine. You can also produce Fighters that then get transferred up to Moscow. UK air based there can provide the attack power for Infantry or Mech coming up from the south, while being available on defense for the capital.
There (may) be a US fleet off Gibraltar or in the channel. If Germany still has some navy or a lot of planes, or if Italy is too tough to attack in the short-term, then you may be stuck a few turns until you can build up your power some more. Be sure the Allies are holding both Gibraltar and Morocco so you can deny Italy 2 of its NOs (this assumes you hold Egypt). If the Allies decide to attack Italy, you can park your fleet inside the Med next to Gibraltar and place an Air Base there to support a Fighter scramble. If the Axis took Morocco and the Allies took it back, awesome! Build an Air Base in Morocco as well and you can have up to 6 Fighters scrambling on defense, this is 2 IPC less than the price of two Carriers, and the two Carriers only give you 4 Fighters on defense. With your capital ships sitting there you deny Italy another one of its NOs, in the meantime, you can dribble in some subs to keep the Italian fleet down and convoy away their money. If the Axis start adding Destroyers to the Med, you have all those Fighters there to support Allied Subs on the attack.
If you’re not going to hit the Med, then you either need to get the US fleet into the Channel so that the UK can make direct drops into France, or you have to move up to Norway. If you go the Norway route, then I recommend that the UK places an IC in Iceland so that the USA can shuck troops E. USA -> Iceland -> Norway rather than E. USA -> Gibraltar -> Norway. Shucking through Iceland is more efficient since you won’t have to leave ships behind to guard the TTs at the halfway point like you do going through Gibraltar. Landing in Norway also takes a German NO, so it effectively cancels out the loss of Leningrad. This also provides more immediate relief to Russia since German units will have to be left behind to counter the Allied presence there. If you can hold Norway right after taking it, build a Naval Base there at a minimum so your TTs can head back to Iceland in 1 move in future turns. Then you can make an IC later. If it’s safe, you can have the first batch of TTs go to Gibraltar in order to still be able to reach E. USA in two moves.
You’ll have to be very leery of what Russia does while this is going on. Once you’re down to just having Moscow and Stalingrad as your ICs, you can keep stacking Infantry in Moscow while you place Mech in Stalingrad. Possibly you can start to work a little ART into the mix. Use your air power in making local counter-attacks on places that only require you to commit about the same amount of troops that Germany will lose. If you have access to a battle calculator you can figure out exactly how many men you can spare to make counterattacks while giving yourself 95%+ odds at holding Moscow. But if a German stack is right outside Moscow, I think the general advice for Russia is to continue to turtle as much as you can until you have enough units that you can challenge the German stack directly.