Suprdav - yes, it's possible if you can pull a small bit of the existing cable out of the wall to work with. The easiest way would be to go to Radio Shack, Wal-Mart, or your local "big box" store, and purchase a new plate that has the female connector on both sides of the plate (basically, a barrel connector mounted to the plate), plus a new push-on male connector for the size of cable you've got (there is a difference between RG-59 and RG-6). You can cut off an inch of the old existing cable to make sure you have clean, uncorroded wire to work with. Install the new male connector to the cable, then connect it to the new wall plate. You'd then mount the wall plate to the wall and you should be good to go.

The slightly harder way would be to remove the old connector from the wall plate and buy an identical one from one of the stores mentioned above. If the original cable was installed by the cable company, they used a crimp-on connector and most people don't own (or need to buy) a crimping tool. You can buy a push-on connector and use it.

While the push-on connectors aren't securely connected to the cable as crimp-on connectors are, remember the cable in the wall isn't being pulled/tugged on so it shouldn't come loose. I hope this helps you - good luck! Jim D/Heathsville, VA