What addy said...you want to lay the new liner OVER the old liner. If you do it the other way, the water will flow under the old liner.
Make sure you have good amount of liner overlap. What I have done is laid my new liner over the old one with enough overlap to reach into the pond water. Before you lay the new liner, try to build up a slope of soil under the old liner pitched toward the pond. I would even shape that soil mound in a concave fashion for extra insurance to guide the water away from the edges and down into the pond.
Here's how I transitioned my new bog liner into my existing pond:
In the picture below, you can see the old liner goes up and over the new transition wall between the bog and pond. I was lucky, I had plenty of old liner that used to be under my old waterfall.
Almost done in the picture below: