The City class will operate BAE CMS-1 - which was originally developed for the Type 45. CMS-1 is, in some configuration, running all RN ships - QEC, Type 23, Albion, Argus etc. You wouldn't develop CMS-1 to replace PAAMS as its a completely different function. PAAMS refers to the weapons system architecture (radar, VLS, CMS, firecontrol etc) in the same way that Aegis is a weapons system architecture. Aegis just happens also to be the name of the CMS.HMS Daring Didn’t actually commission until 2009, so depending on how hard she got knocked around during first of class trials and defects she will only have 21 years of hard use in 2030. Young enough and current enough for a sale to Brazil, Chile or Poland to be attractive?
Don’t the City class have a proprietary BAe CMS? They may just further develop that to replace PAAMS though I assume the RN will stay with Aster unless they pay MDBA-UK to develop a replacement.
There's a lot of capability and upgrade potential in Type 45. I don't see any urgency in replacement as others seem to.