Train new data to pre-trained model
It all depends on the specific algorithm you're using. Some of them support incremental learning, while others don't.

For example, in the case of scikit-learn, using fit() more than once on the same model will simply overwrite the model's weights each time (see here for more details). 

What you can do however, is look for algorithms that implement the partial_fit api, and use this to retrain your existing models - see the documentation for a list of algorithms that support incremental learning and thus implement this api.

An alternative solution is to look for algorithms that support the warm_start parameter, e.g. LogisticRegression. Note that warm_start might also be influenced by other parameters, so you need to pay attention to their values, too - e.g. in the case of LogisticRegression, warm_start won't work if you use the liblinear solver (which is the default).