Panic. A huge proportion of the world’s oil passes through the Straits of Hormuz, and if the USSR should end up controlling Iran, it is de facto controlling oil supply to the rest of the world. We saw the panic in the early 1970s through the OPEC oil embargo, and in this situation, it’s the USSR calling the shots.
Pakistan is not going to be a happy bunny. It was on good terms with the USSR, and in 1979, the US embassy in Islamabad had been burned to the ground. If the Soviets control Iran, then Pakistan military government can expect destabilisation efforts from the USA, and uninvited support from the USSR, turning Pakistan into a proxy battlefield. Relations between India and Pakistan, dodgy already, will nosedive. It’s only a few years ago that India intervened in Bangladeshi independence, when East Pakistan decided it would change its name, and the Pakistan Army tried to restore order and prevent Bangladeshi independence through terror tactics against the local populace. When this violence threatened to spill over into India, the India army came and unceremoniously kicked the Pakistan army out. This soured relations between the countries.
God knows how the Iran/Iraq conflict develops. One of the many reasons for the start of this war was Iraq wanting to supplant Iran as the dominant regional power. How that plays out if the USSR is controlling Iran is anybody’s guess, but I doubt it will be stable.
Another factor is the unbalancing of the Sunni/Shia relations. USSR controlling the dominant Shia power will change the power balance. One could argue that by removing Iran’s influence over the Shia, there will be less conflict. More likely, in my opinion, is that we would get Shia Muslims adopting traditional asymmetric warfare techniques.
And this presupposes the USSR is successful. This is not a given. The USA is likely to back resistance, just as it did in Afghanistan. The USSR had a few problems in Afghanistan alone. Now it’s having to deal with Afghanistan and Iran, and is likely to suffer from overstretch. It’s also likely to have problems with its own Muslim population, many of whom have Shia affiliations.
Just for added complications, the Kurds in Turkey, Iraq, and Syria are now sitting in land right next to a trouble spot, and this could easily blow up into something unpleasant.
Those people with investments in Iran (China and India being of greatest interest) are likely to get very twitchy.
Israel is involved in Lebanon at this time, and I suspect it would be really unhappy about the USSR trying to take over Iran. The Bushehr Nuclear Power Plant was well under construction. In OTL, this construction was disrupted by the Iran/Iraq war, but I’m not convinced outside parties would be quite so keen to bomb property of the USSR, so the plant, after a hiatus, probably gets built.
Just to add to complications, in Saudi Arabia in OTL in 1979, the Grand Mosque in Mecca had been seized in an attempt to overthrow the House of Saud, hostages taken, hundreds killed, and the Saudi military made numerous unsuccessful and unprofessional attempts to retake the Mosque, until Pakistani Special Forces dealt with the issue. In OTL, this led Saudi Arabia to adopt a less tolerant view of things, and religious laws became severe. If the USSR is active in Iran, it is likely that Pakistani Special Forces won’t be involved, it seems improbable that the Saudi military would make much headway, and Saudi Arabia couldn’t allow the occupation to continue. Which probably results in them asking for US Special Forces to do the job. In OTL, even the rumour of US involvement caused anti-American outrage in much of the Muslim world. If US troops were actually involved in an attack on the Grand Mosque in Mecca, things might spiral out of control very quickly.
Other than that, I don’t think there would be much effect.