If you close an old credit card and open a new one, your credit history will reduce and so your score will be lowered. However, if you can switch your old credit card account over to the new one, then your history will remain the same.
If you are switching credit cards within the same bank, they might agree to keep the same account open for the new credit card.
As long as you are smart about it, switching credit cards shouldn’t be too detrimental to your credit score.