I have a residence card for my first employer. I changed my employer. Can you not exchange the card? Do I have to apply for a new employer?

If you are staying in Poland based on a temporary residence and work permit, issued under employment with an Employer with whom you no longer work, you should report this information in writing to the office. You will find the template HERE.

Whether you have to apply for a new permit or not depends on the type of permit you have. However, as a general rule, if your employer and certain terms and conditions of employment are indicated in your decision, the permit you have only allows you to work for that particular employer and under the conditions set out in the decision. So if you have changed your employer, you should apply for a new temporary residence and work permit.