You can have more than one credit card with Barclaycard but usually not within a year. Look at your credit reports to see how they look like. If there are too many recent applications in general and with discover in particular, 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.