Credit card replacement brick wall

My credit card is peeling apart and as a result is having trouble fitting into card machines etc when paying. It expires in 9 months time. I have asked the Premier "team of bankers" to organise a replacement card for me, at no cost obviously as it's not due to loss or negligence. I am told that I can do it online, but I have to first cancel my existing card, then order a new card. How am I supposed to pay for things daily if I cancel my existing card? Why must I go without a card and ability to spend/purchase when the quality of the card is so poor that it does not last until expiry date? How is it in this day & age, I cannot receive a replacement card first, then cancel the bad card? It's absurd and there must be a solution, besides moving banks.