First, the YPbPr (red-green-blue) is a component input, not composite. Composite is yellow-red-white.
The two are not compatible and cannot be substituted. With component, all 3 colors comprise the video signal and none of it is audio. With composite, the yellow connection is for video and red+white are stereo audio.
But you can still use the RF output of the unit with your new TV. Connect the coaxial RF out jack (like an antenna jack) to the TV's antenna jack and put the TV on channel 3 or 4. Video and audio from the DVD/VCR will be on one or the other.
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Followup: I also thought of a composite to component converter but didn't bother. As suggested above, it only deals with video, and it would cost you anywhere from about $30 to hundreds. The RF option is totally free if you have a short antenna cable with fittings on both ends. If not, a dollar or two in the electrical department of a hardware store.
Also, are you SURE your new TV does not have a composite input? Not impossible, but a bit unusual. Good luck.