Is this sentence OK?
That happens in other countries, but doesn't here.

Question

Answer

It would be better to say that happens in other countries but it doesn't here.

Answer

That happens in other countries,but it doesn't here
..but it doesn't happen here
Either of both is correct.

Answer

It would be clearer, obviously if you repeated either the object or the verb

.. but it doesn't here.
.. but doesn't happen here.
.. but it doesn't happen here.

However, your sentence is just about ok. Others may disagree, but I think it's acceptable as it is.