You can have more than one credit card with Barclaycard but usually not within a year. Look at your credit reports to see if everything is correct on them. If there are too many recent credit card applications, you are at the risk of being denied. Also, your current Barclaycard credit accounts should be in good standing and in active use if you want to qualify.
If you need a travel rewards credit card, there are good alternatives out there. Or if you want to wait, we would recommend you to wait at least 6 months before applying for a new Barclaycard card.