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I wouldn't worry too much right now. Sometimes it can take up to 2 weeks to get your new card. CapOne is one that comes to mind that can at times be slow in regards to shipping.
Are you counting days, or business days?
After 15 business days give them a call to see.
Some banks are just slow with shipping. I've had cards take two weeks before. Synchrony isn't known for expedited or quick shipping.
I'm sure it will arrive within a few days or less. I doubt it is lost. While that happens occasionally it's not that common, and more likely the lender just took their time sending it out.
I was approved for an Amazon Store card (Synchrony). Never received the actual card in the mail. Not a big deal because you can't do anything with the actual card. But it bothered me. Called CS @ Synchrony requested they send a new card - they were happy to do that. Never got that one either. This was all within the last few months. Have you gotten any mail from them concerning your card? You might login to your account and double check your address online. Good luck. Synchrony seems to be going through some turmoil lately.