Can I use an exiting SIM card in a non-contract phone?

I use an AT&T Windows Phone and I need to switch to a new AT&T phone. I use the Lumia 1520 right now, but I would like to switch to the Lumia 635 which is a no-contract smartphone. I am wondering if I can simply take the SIM card out of my Lumia 1520, which has a two year contract, and put it into the 635 and be able to receive texts, phone calls, and use data.

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