Both the photocard and the paper counterpart are required in order to pay the fine and have penalty points endorsed. It is advisable to apply for a new licence straight away, as a new licence may be issued before the due date on the Conditional Offer of a Fixed Penalty Notice expires. You should also inform the issuing office.
If at the end of the 28 day period you still do not have your driving licence and therefore you are unable to make payment, a police report will be raised for the Procurator Fiscal for their consideration of prosecution.