The problem is that the Counties were designed around the Seaslug missile, and missiles become obsolete much faster than warships. Seaslug was very much first generation, and much better alternatives came along fairly quickly.
So what to do with the Counties? Not a lot. You could have rebuilt them to take much more modern missiles, but that would have been expensive, and they were very large vessels for their role.
You would be better off starting again from scratch.
What to do with the counties?
Late 60s there is a need to bring something into service that can deliver Sea King to parts of the North Atlantic. The hugely expensive (more than the cost of brand new County) Blake and Tiger were the first answer to that, the flight deck and hangar weren't great but the real problem was their huge crew and unreliable machinery and main guns.
Strip out sea slug from the counties, you get a huge amount of space available for aviation stores and workshops, an extended flight deck and hangar for two Sea Kings. I know the counties weren't cleared for Sea King, but that was the existing fight deck. If you could squeeze four over the quarterdeck of Tiger, there was room for two on a county.
More importantly you release a hell of a lot of topweight, by losing directors, launcher, all those giant missiles and their complex movement / storage / fire suppression system. Substantial crew reduction too. You don't need to fit a modern air search system, datalink and communication facilities as Tiger and Blake required - the counties already had all that.
Then they needed to bring the Ikara into service and spent a ton of money (£102 million - the cost of a CVA-01 or six new counties) adapting eight Leanders to carry it at the loss of many systems.
With the counties you've got all that weight and space available from the huge sea slug launcher which you can plug with Ikara. You've got the Sea Slug ready use lockers right alongside to house the weapons and they already had ADAWS. Far less cut and shut and now one ship is doing aviation and Ikara in the ASW groups - so cheaper.
Then in the 70s Lynx, Exocet and Seawolf are looking for homes in the ASW group, more Leanders are cut up to bring them in. The counties still have systems like B-turret to be dropped in favour of the missiles. Now two counties are doing the job of one Blake, one Ikara Leander, one Exocet Leander and one Sea Wolf Leander. Huge savings.
Then we start the development of the Type 22's to provide command and control for complex ASW missions and eventually the towed array sonar. The biggest problem the T22 had with that mission was their gas turbine machinery which limited the use of towed array, noisy brutes. So more Leanders are chopped up so their quiet steam propulsion can get more from towed array. But they are so small they get stripped of pretty much everything else. So you have two ships required to operate the towed array, command systems and a smaller aviation complement. Expensive way of doing business into the 80s and 90s.
The counties have more than enough flagship space to accommodate the T22 command facilities they can operate towed array as they have steam propulsion for quiet towing. When Ikara falls out of fashion you've got top weight and space in the right place to fit towed array on the quarterdeck.
Just as the last counties were being commissioned there was absolutely a need for a large volume hull with mixed machinery and good seakeeping, top weight reductions and space for ASW sensors, command and control.
You don't have to build the T21s as you've got plenty surplus general purpose Leanders not getting chopped up to carry ASW gear. Vosper proposed such an ASW fit, and of course the Chilieans went and did parts of it. So it's not beyond the reach of imagination.
They could have served well into the 90s, instead of their early disposal.