Operation Ajax, known in Iran as the Mordad Coup, was a coup d'état orchestrated in Iran by the Shah, Mohammed Reza Pahlavi, British oil companies, and elements of the CIA and MI6. It deposed the populist-nationalist and allegedly pro-Soviet prime minister of the country, Mohammed Mossadegh, and replaced his government with a pro-NATO regime, which would end up in the Shah's hands for the next two and a half decades until his deposition.
But what if Mossadegh had not been deposed? Say, through the coup failing, its true intentions being exposed, what reason have you. He stays in power for longer, perhaps until his OTL death in 1967. But he still finds out that he was the target of a coup attempt.
I suspect that this new situation would be cataclysmic for the Middle East. If a Soviet-friendly guy is head-of-state of Iran, he could gradually grant access for them to Iran's oil shales in the southwest.
Could the Shah have been deposed later down the line? How close to the USSR could Mossadegh have strayed?
What are the effects on the Suez Crisis, which may still be scheduled to happen three years later?