Credit card expiring - new one likely in the mail

With a credit card expiring soon and the new one very likely already in the mail, it's very likely it won't get here before the current card expires. This is also the only CC I use/have. What are my options in this case? Would it be best to ask my bank to send a new one via courier (I'm happy to pay the delivery), or is this just a tough luck scenario and I essentially won't be able to use my card until the new one is delivered by CP?