If the model is trained with 6 features, it means that this model is like a function which requires 6 arguments. For instance the model might calculate the answer like this:
answer = 0 * f1 + 1 * f2 + 0 * f3 + 5*f4 + 0.5*f5 +10*f6
Obviously there's no way to know the answer of this function without knowing all its arguments.
Another way to look at it: given a model trained with a particular set of features, let's assume that it is possible to apply the model using any subset of these features and still obtain the prediction. This implies that it's possible to remove all the features. Therefore this model is a magic box able to predict reliable information from no information at all. I hope it's obvious that this is not possible.
In order to be able to predict with 3 features, the only way is to train a model with these 3 features.