How to update a value, given a key in a hashmap?

Suppose we have a HashMap in Java.

How do I update (increment) the integer-value of the string-key for each existence of the string I find?

One could remove and re-enter the pair, but the overhead would be a concern.

Another way would be to just put the new pair and the old one would be replaced.

In the latter case, what happens if there is a hashcode collision with a new key I am trying to insert? The correct behavior for a hashtable would be to assign a different place for it, or make a list out of it in the current bucket.