I had a pap back when I was under 65. They (who, not sure) said the results were lost.
Made an appt and went back after age 65, when I dropped my union insurance and took
Up another secondary. The lab (Quest) denied payment because it was billed to my
Union insurance. Do I now have to have my new company pick up the tab for this
Mistake? It's $195.00. I really don't want to pay it, but I also don't want to end up in
Collections.

The provider that did the initial pap and lost it, needs to cover the second pap at no cost. I've worked in a facility and this does happen. Usually it's not "lost" but maybe two letters transposed in the name, so it has to be rejected from the lab. But the initial pap was turned into your insurance and the 2nd should be done at no cost to you.

If you can prove who lost it, they should pay.

But, what insurance do you have now ? If in the US, would you not have medicare ? And a medicare suppliment. IF so why would it not be covered