How to use published regression models in the process of model development?

What is the best way to use information in already published works in the process of prediction model development?
Suppose that we have access to several published regression models with different independent variables (Models can have some common variables). How can we use the estimated parameters of these regression models to improve our prediction model as compared to relying only on local data?

You can externally validate the already published regression models using your local data and if necessary you can update those regressions equations for your settings.

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Thank you, but it is not clear to me how it should be done?

I thought something like the approach in the following paper (Page 17-18, Eqs. 7-8 ) might be a good idea:

[1907.06560v4] Deriving Priors for Bayesian Prediction of Daily Response Propensity in Responsive Survey Design: Historical Data Analysis vs. Literature Review (arxiv.org).

But I am not sure if it is the right method.