No need to replace your Panasonic 1080p Full HD or even if you owned a Panasonic 720p HD Ready Spec plasma television where they would both work perfectly fine with the NowTV Stick (assuming you have a decent WiFi reception where the television would be located in the Home).
With regards to HDMI to VGA or Composite or SCART converter boxes, just be aware some are a little flaky in operation and may cause HDMI HDCP error messages or audio lip sync problems.
If you can find a reliable HDMI converter box that can pass the NowTV Stick HDMI digital signal cleanly through it then there is no reason it will not work with your 480p SD Plasma TV.
Hi again @schnapps
Unfortunately, my Panasonic plasma is neither Full HD nor HD Ready ... it's PRE- HD!
The wi-fi reception is very good.
I've tried switching between an HD and non-HD program (on BBC), they both play okay and look exactly the same (but, obviously, it's not in HD).
The possible error messages & lip sync problems sound less promising!
Sorry i missed read your post and thought you owned two Panasonic Plasmas TV's (one 1080p and the second 480p SD).
Where the second 480p SD TV was using the White NowTV box.
If you can find a correct spec HDMI converter box and it's reliable, then it should work OK with the pre HD plasma television, though you are only getting 480p signal out of the converter box, where the Stick can max out at 1080p (720p on NowTV streaming service or 1080p with the NowTV HD Boost Pass) if connected to a higher resolution television.
Anyway will leave it to you to do your research and find the best solution on using the NowTV Stick.
From what i have been told NowTV will be switching off the White version of their boxes completely on the 6th of October 2020.
So you won't have access to any of the third party Apps off the White Boxes after the above date.