Or, I think it's rare but has happened, one new party wipes out an existing older party and most of the old party's new adherents go to the new one. IMO that's more of a re-brand than a whole new party.
100%.
Federalists were the first conservative (here meaning traditionalist) party, who basically disappeared after the war of 1812. The Democratic-Republicans (Jeffersonian Republicans) split during the 1824 election; party loyalists made the Democratic Party, and those who weren't went to make the National Republican Party. The NRP only existed for ~8 years before it combined with former Federalists and unhappy democrats to make the Whig party, which then became the GOP.
Given the policies, I think an arguement could be made that the Whigs might be the only true "new" party in our history to ever gain any power. The Republican party basically started as "Whigs who openly opposed the expansion of slavery", so that seems to be more rebrand than new concept.
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To the broader topic of Elon and third parties; I think Elon could make a viable third party, if it focuses energy on Congressional seats as opposed to the Presidency. We've seen how "libertarian"/independent Senators/Reps can have outsized impact in legislation, simply because margins are so thin. If Elon managed to get 2 or 3 Senators elected they could have a huge impact.