It depends on the type of debt relief you're participating in. Talking with a credit counselling agency shouldn't affect your ability to use existing credit cards, but a debt settlement and management program might require you to cancel your credit cards or could result in credit card companies cancelling your cards.
You might be able to apply for additional cards after you've finished your debt relief program, but you won't be able to use your old ones. You may then want to consider secured credit cards designed to help you rebuild your credit score.