Do I need Airport Extreme to print wirelessly from HP 1012?

I have been printing from my MacBook Pro Laptop (10.6.8) to an HP Laserjet 1012 via an Airport Extreme base station. I use Comcast as my internet provider and recently they sent me a new modem (Xfinity Technicolor) to replace the old one. The new modem has wifi built in, so they told me that I don't need the Airport Extreme anymore. Everything is working fine, except now I am not able to print wirelessly. I have pluged in my printer via USB to the new modem. Will my Laptop still be able to connect to the HP 1012, or did I need to keep the Airport. If so, can I have both the new modem and Airport running at same time? Thanks!