what do you mean by When I shut down the Apple imac running the latest s/w tp link will not shuy down ? which one can't be shut down? a bit confused.
what model number of your router?

Sorry for the confusion. Here it is spoken in a different way.

I select 'shut down the computer '
It proceeds through shutting down the programs that run in the background including TP-Link. However TP Link refuses to shut dowm. So I have to force quit TPL in order that the computer can shut down.

which utility you have installed on the computer? can you show us some screenshots?

Thanks Flying snow,
Version 1.16.1214 Driver version 2.08

What would you like screenshots of?

Version 1.16.1214 Driver version 2.08 what is it this for? it is not a TP-LINK, you have a TP-LINK router C5? shutting down computer will need to shut down router as well?
And what TPL means? sorry, not following you.

The program TP-Link usb printer controller on my computer that links it to the router is the issue I am assuming, not the router.

we can quit the controller then shut down the computer. As when we close the windows, but the program is not actually closed.