This is called Online Learning, as opposed to Batch Learning. It’s a somewhat neglected topic in terms of available packages, but there is one here (it has decision trees, not RF):

https://github.com/online-ml/river

There is a nice interview with the author on the ML Podcast

https://podcasts.apple.com/us/podcast/the-machine-learning-podcast/id1626358243?i=1000577393019