Here’s a thread discussing this topic: Composing Stan models (posterior as next prior)
There’s a variety of posterior-to-prior approximation methods discussed there but note Michael Betancourt’s warnings on losing information when you try to run things as separate models and advice to simply re-fit the model when feasible. In the scenario of a second experiment, you’d want to take your single-experiment model and for every parameter that you previously had as a single value, model it instead as having a distribution across studies with a mean and variability. So, if the experiments were in my field, cognitive science, I’d usually have multiple human participants in each experiment so for a given experiment’s model I’d have a parameter for the mean-across-participants in the outcome, and to make a single model of both experiments I’d code this mean-across-participants parameter as itself deriving from a meta-distribution with a meta-mean and meta-variability. With only two experiments, you’ll want to think carefully about the prior you put on the meta-variability parameter, as this will effectively reflect how much inference from one experiment will influence inference in the other experiment and vice versa. I haven’t seen any explicit case studies of this scenario, but possibly @betanalpha could chime in on whether my suggestion makes sense.