Cab 13 of Richmond has already been upgraded to FTTC, but it looks like Kirby Hill is too far from the cabinet to benefit. It looks like the cab is at the start of Cutpurse Lane, on the edge of Richmond.
I'm not entirely convinced that Clannet covers the area either - judging by the Superfast North Yorkshire website. Their new Where/When map is really hard to use, but I suggest you do something like this...
1. Go to http://www.superfastnorthyorkshire.com/wherewhen
2. Zoom the map until you can see these locations on-screen at the same time...
Richmond, Gilling West, Ravensworth, Melsonby
3. Click on the dot at the centre of Melsonby.
This will bring up a box labelled "Multiple Service providers selected (1/2)", and display details for BT's fibre service. The map will show areas covered by this cunningly shaded white - so almost impossible to see on the map.
You'll note that the white "superfast" coverage doesn't extend far out of Richmond towards Kirby Hill - a little over 1km. Any improved coverage compared to ADSL, even if not quite superfast, probably runs out at 2km, or just over a mile.
4. Click on the right-most ">" symbol next to the "(1/2)"
The text box will now change to give Clannet details, and the white-shaded areas on the map will change. To me, it looks like they cover areas to the east of the A1, and north-east of the A66.
I think the best that you can do, to find out the truth of the matter, is to contact Clannet themselves.