How to control for Co-variate shift in test data set compared to train data for regression task?
There are several options:

Change the training dataset

Use some of the test data as training data. This the best option since it better models the problem you are trying to solve.

Since it happens over time, take only the most recent data for training.



Manually engineer features. If you have knowledge of how the test data feature values are different, then explicitly put that knowledge in the model.

Increase regularization. For scikit-learn's ElasticNet, increase alpha hyperparameter. Unless your validation dataset is similar to your test data, you'll have no evidence that this will improve the modeling.

Switch algorithms to one that is better at generalization. Possibly, Random Forest could be better than regularized linear regression.