أريد أن أطلب بطاقة جديدة

Use it when you are standing at a counter or on the phone. You can add the type of card after the word كارت (kart). For example, say كارت بنك (kart bank) for a debit card. If your card was swallowed by an ATM, this is your magic sentence. It is simple enough that you won't stumble over complex grammar. Just state your intent clearly.

Use it at the bank if your card expired. Use it at the club or gym for a membership ID. It works perfectly when calling customer service hotlines. If you are texting a concierge or a business, it is also appropriate. It is the 'bread and butter' of administrative requests.

Don't use this in a very high-level diplomatic meeting. It is a bit too direct for 'Old World' formal letters. In those cases, you would use أود التقديم على (I would like to apply for). Also, don't use it for business cards. For those, people usually say كروت شخصية (kroot shakhsiya). Using it for a birthday card might also confuse people; that is a كارت معايدة (kart mo'ayda).

In Egypt and much of the Levant, 'Kart' is a borrowed word from French/English. It replaced older terms as digital banking took over. Egyptians love efficiency in service interactions. Being direct with عايز is not considered rude if your tone is friendly. It shows you know exactly what you need in a busy city.

If you are a woman, you must say عايزة (ayza) instead of عايز. In more formal settings, you might hear حابب أطلب (habeb atlob), which means 'I would like to request.' If you are in a hurry, you might just say ممكن كارت جديد؟ (Possible a new card?). Adding لو سمحت (law samaht) at the end makes you sound like a total pro.