Mike what ship and period are you modeling?
I ask as Fire-control in the Tribals was improved throughout the war as they went through a lot of alternations especially because they were found to be particularly vulnerable from air attack.
I'll just try to relay some of the wartime changes to you briefly.
'As fitted' the Tribals had what I stated above, A separate Rangefinder-Director Mk II aftermost on the bridge which was behind a SEPARATE Director Control Tower or DCT.
The first destroyers to get a combined DCT with rangefinder was the commandeered 'Havants' or Brazilian H's.
The first class built for the RN from the get go with a combined DCT & RF built in was the L class (this being later abandoned in the various wartime emergency classes).
As the war progressed the Tribals began had their original Rangefinder Director Mk II replaced with a RangeFinder Director MkII (W). Which was one simply with a windshield attached to the rotating structure and, when fitted, the earlier fixed drum shield was removed.
When X turret was landed the new twin 4-inch mounts operated in barrage fire through this existing range finder director with some clever trickery to compensate for the different elevation and fuse settings required for the 4-inch shells over the 4.7-inch.
As the Tribals went through further refits then their 'as fitted' Rangefinder Director MK II got replaced by the better protected R/F Director MK II (W) above then later still got the addition of radar Type 285.
Some Tribals later still got the R/F Director MK III (W) with Type 285 also.
Calling it a HACS would be wrong. It does control HA fire, but it is no HACS merely an improved Rangefinder Director with windshield and with Type 285 gunnery radar added on top it with the yagi aerials.
So if Friedman is calling it a HACS he's a very naughty boy!
So then to answer your original question certainly by 1941 a ship such as
Ashanti had a Rangerfinder Director MK II (W) with Type 285 radar in front of her original DCT which is retained.
Obviously it differs for different ships and different periods, but generally what I went through above is the course they went through during the early war years.
Plans of both the DCT and Rangefinder Director Mk II are given in Peter Hodges book and also the details as to how they were improved during wartime.
Cheers
Laurence