You can't sell it privately if there's outstanding finance on it.
You need to settle it first.

With trading in.
Generally, you and the dealer will agree a deal on the new car, you will usually not have to hand over your trade in until you pick the new car up.

If there's a big factory build wait, they'll factor in this when valuing your trade in.
If your old one was a lease and has to go back on time, I've known dealers to loan out a car.

If there's outstanding finance, they will settle this out of the trade in value.
If it's more than the value of your trade in, you'll have to refinance the difference.

There is someone on this forum looking for a Panda Easy.
https://www.fiatforum.com/panda-iii/454809-brink.html

I seem to remember you writing you are NHS staff?
Have a look here
http://www.nhs.motorsourcegroup.com/
We saved just short of £5000 on a new Suzuki Vitara a few months ago through them.
£1730 off a Trofeo.
If you're interested, PM me and I will send you a direct contact that helped us and explain how it all works.

Brilliant! I’ll PM you now! Thanks again!