I'm afraid not. The vast majority of conifers will not regrow once they've been cut back hsrder than the innermost green leaves.

Your only option is to remove the tree and start again

Thuja, however is one of the genera able to grow back, though it can be slow. New growth can be blocked by lack of light--as often happens next to a wall--or lack of nutrients. I would clean up the pruned area, removing any dead twigs and branches, lightly prune back the rest of the bush, to direct energy into the dormant buds, and feed it lightly in spring with an organic source of nitrogen, such as blood meal, or fish meal. Hopefully that will start some growth in the damaged area, or at least help the surrounding foliage to cover it.

Thank you for the advice - it is much appreciated

Do you have a source for your view that Thuga Occidentalis will grow back from old wood Tugbrethil or have you specific experience of doing this. The reason why I ask is that on Googling opinion seems to be well split on this... some saying it will regrow some saying it won't.

I saw these trees in Redwood City, doing this, and the closely related Platycladus orientalis that grows everywhere around here does this easily. The rule of thumb--not always consistent--is that conifers that branch in whorls--spruces, firs, most pines--will not stump sprout, while more random branching kinds--Cypress family and Redwood family--do.

Well I guess it may be worth Douglas giving it a try but then again as he says it is some years since the damage was done and there's no sign of regrowth personally I'd give up and replant with something new.

It's something that may be easier for the tree in warmer climates. Another possibility is to--carefully--retrain the tree from a formal column to a more naturalistic design. Both options save the tree--assuming they work--but take a good deal of time to show results. It is telling that even though they stump sprout, the advice on Arborvitae (Platycladus) trees is to never prune them!