Did Peter expect Jesus to return to Israel immediately?
Yes, Peter expected the Lord's immediate return to the nation of Israel if they would repent. Yet he also recognized that before this restitution, Israel must pass through seven years of tribulation, the times of restitution of all things, when heaven must receive Christ until that time.
Les teaches that Peter did expect the Lord's immediate return to the nation of Israel if they would repent. However, Peter also recognized that Israel would have to go through the seven years of restitution of all things. Les explains that Acts 3:20-21 continues the thought: God shall send Jesus Christ, whom heaven must receive until the times of restitution of all things. The word "until" is a time word, showing Christ will not stay in heaven forever but will leave heaven again. Les identifies the restitution of all things as the Tribulation, the seven years pictured by the scroll and seals of Revelation chapter 5, the mortgage Satan has held since Adam fell. The earth has been under the curse nearly 6,000 years, but it will be restored to its Edenic condition. So Peter expected an immediate return if Israel repented, yet he also recognized the necessary seven years of restitution.
Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord;
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