@Grug 

Hi,

Did the switching of Internet providers necessitate the exchange of any hardware?

In case it did, then please perform the following test.

Unplug the mains power adapter(s) or mains power cord(s) of that newly installed hardware and then observe whether the Powerline lights of the Powerline devices come ON after relocating or not.

  @woozle 

Hi,

YES, there is new hardware, and testing what happened when I switched things off, I WAS able to maintain the powerline connection after relocating the extender.

The dilemma now: the thing I switched off that allowed the extender to work was the router that the adapter is plugged into. There are two routers in the house, and in order for them not to conflict, the second router (where the adapter is attached) has a different IP address to the standard. The adapter can't plug in to the OTHER router, as it is a starlink. Am I right in assuming that I need to somehow change the IP for the adapter/extender so that it gets along with the router, or will it just start conflicting with the starlink instead??

  @Grug 

I didn't explain it in my first post, but the reason I suggested to unplug the new, previously not existing hardware was that one of the main culprits affecting the performance of Powerline adapters are power supplies (or call them AC/DC adapters or just power adapters) that generate a lot of electrical noise in the electrical circuits (the wires running through the walls of a house).
Powerline adapters use these same wires to transport their data signals and increased electrical noise from other electrical appliances diminishes the quality of the data signals of the Powerline adapters.

So, what can be done about it?

If the power adapter of the new router is plugged in a wall socket very close to the TP-Link Powerline adapter, then you can try if plugging that router into another wall socket a few meters away might be just enough to allow the Powerline adapters to work in their original locations.

Replacing the power adapter of the new router would be another option, but that is easier said than done, because nobody knows in advance whether another power adapter would be better or not.

Can you maybe compare the specifications of the old router's power adapter and the new router's power adapter and their plugs?

If you are extremely lucky, then they might match sufficiently. (like my example shown in the pictures below)