Instead of building more at the city centre station (which is pretty constrained - look at how expensive it is to put one additional platform into a space occupied by a car park - it'd be a lot more expensive to build over the river etc) you could free up a lot of platform space by either extending trains through to Neville Hill or a terminus at Thorpe Park (as was planned) - there are six through platforms so even if you write off one as being clogged up by London terminators and one spare then the other four through platforms ought to be able to allow most of the (non-Kirkstall) services to become through trains
Trams will always get suggested but it'll be hard. Tyneside/ Manchester/ Wolverhampton/ Croydon were able to build theirs mainly by either directly converting heavy rail services or by using abandoned rail alignments - Sheffield has struggled comparatively because (other than the Meadowhall line) our trams are stuck in road traffic - I think that any Leeds line would be similarly at the mercy of congestion (e.g. Headingley is an obvious corridor to try to justify light rail to soak up large passenger volumes but how do you run something that isn't going to get stuck in the same A65 congestion?
9 is still going. But has a few detours away from the ring road. Like one to Moortown Corner
The problem with the geography of Leeds is that you can either run a relatively "fast" service around the ring road (depending on traffic/roundabouts, of course!) or you can try to link various places together but it's hard to do both.
Some cities have a traditional kind of ring road that takes you through various traditional suburban centres (or where such post-war things have been built next to the ring road) - for example I grew up with the Outer Circle in Edinburgh which ran through the heart of Leith/ Portobello as well as serving the modern shopping centres at Cameron Toll/ Wester Hailes without much of a diversion
Leeds though... the 8/9 were able to serve the modern shopping centres at Seacroft and White Rose with only a minor time penalty, but it's more of a diversion to serve Horsforth/ Moor Allerton/ Garforth/ Pudsey and a lot further (from the ring road) to Armley/ Headingley/ Hunslet etc, plus a lot of fairly empty space between Crossgates and Middleton (the south east of Leeds is the flood plain, so there's not many people living in the land between the A64 and M1).
Dundee/ Glasgow/ Manchester/ Sheffield etc had long running "outer circles" that had the advantage of serving at least one major hospital, but that's not the case in Leeds (the Infirmary is in the city centre and Jimmys is more "Inner City" than "outer circular"
So is a ring road there to properly link the suburban centres together or to link ring road junctions together for people to use as a connection between different radial routes (e.g. the A61 to the A65)?
When I lived in Leeds (twentyish years ago) there were a lot more "radial" routes - e.g. the half hourly 81/82 from Pudsey to Holt Park - but such secondary routes have dwindled away as they have in many First operated "networks" in that time period