Yes, though that might depend on your definitions of both long term and vaccine. There is actually a quite interesting body of literature surrounding these developments, so it might be worth doing some searches and some reading.
Re:The end of the pandemic is near
by loveistheanswer on Sunday May 30, 2021 @10:27AM
(#27333462)
Do you have any sources for long term mRNA vaccine trials on humans?
My searches seem to indicate there are none, other than the preliminary, limited scope short term trials
Have there been any long term human trials of mRNA vaccines?