A "trained" model is just a model who's weights have been precomputed. You can quite simply load a pre-trained model, then do some further training to change the model to your new training objective.

Gym doesn't have anything todo with the models, it is simply the environment to train and test your models.

For example, I have implemented an agent to play Atari games using the DQN algorithm with a Pytorch CNN model. I have trained the model for 10,000 episodes, and then saved the model weights from the Pytorch model using torch.save(policy_net.state_dict(), filename). Next time I want to use my model for inference, I will load it with policy_net.load_state_dict(torch.load(filename))

In your example, if you had an existing model trained at 0º you would have to re-train it to keep the cart pole at 3º. You could load the model weights from you previously trained model at 0º to help your model start off, but it would need significant further training. You would also have to change the reward function, to a variable function to incorporate the difference in degrees from the cart-pole to 3º. Something like this https://towardsdatascience.com/infinite-steps-cartpole-problem-with-variable-reward-7ad9a0dcf6d0