When Theresa May faced an internal vote of no confidence and won in December 2018, she was safe from facing another one for a year.
Does a new leader of the Conservative party enjoy a simlilar period of immunity from a leadership challenge?
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The 1922 Committee doesn't publish the full rules with regards to no confidence votes or leadership challenges, so it's difficult to independently confirm this.
According to BBC Political Correspondent Chris Mason in a tweet, a new leader does not enjoy the one-year immunity from a non-confidence vote. This immunity only applies if they win a no-confidence vote that comes later.
Quoting from this Sky News article:
Currently, Tory leaders who win a confidence vote - such as Mrs May last December - enjoy a year's protection.
But this does not automatically extend to an incoming leader.
This means that Boris Johnson or Jeremy Hunt could in theory face a challenge as Tory leader within days of becoming prime minister if 47 Tory MPs - 15% of the parliamentary party - write to the 1922 chairman demanding a vote takes place.
I think that the two current answers are technically true, there are no rules that forbid an instant challenge to a new party leaders authority.
However just because there are no rules does not mean that they don't enjoy a period of immunity. The party would have just gone through a 'democratic' leadership election. Both MPs and party members would have helped to choose the new leader. So an immediate challenge would almost certainly fail. This would then give the leader a year of immunity.
For a challenge to be launched it would need to have a feasible chance of passing. A new leader would need to do something that would lose confidence for this to happen.
So I think that while there is no procedural 'period of immunity' there is a political one.
It's also worth noting that the conservative leadership confidence vote is different from a parliamentary confidence vote. In theory, a new Conservative party leader can't become PM until they have 'the confidence of the house' this is not a given currently. Quite what happens if they don't get the confidence of the house is anyone's guess.