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how can I use an existing subwoofer with a tv soundbar that has none?

I have a subwoofer from an old sony surround system that I want to use with a tv sound bar that I got for Christmas.  The subwoofer is stand alone (has its own independent power input) and connects to the surround system via a coaxial speaker cable.

If the sound bar doesn't have an output jack to plug in additional speakers then you won't be able to use it. Other than opening up the sound bar, disabling one of the speakers and using the leads from that speaker to send an audio signal to the sub.