The performance of the train will be restricted until the new signalling comes along. There might be small gains arising from modern traction equipment and modern braking. Conventional Tube signalling is designed with calculated overlaps. The principle is that engineers calculate the worst case speed a train with no passeners could be achieving when it strikes a trainstop, taking account of variable such as traction voltage, wheel diameter, gradient etc. This speed is probably unrealistically high as high traction voltage, large wheels and empty train are unlikely to happen together. The calculated speed is then used to calculate the worst case stopping distance for a crush loaded train. This distance, plus a margin for error becomes the overlap.
For the new train on existing signalling, some of the variables can be eliminated. modern traction equipment tends to provide a constant performance irrespective of voltage (within limits of course!) and the tractive effort curves can be set, so, for example, there could be a very high rate of acceleration up to, say, 30 mph with a ceiling on speed. This is what was done for S stock prior to ATO. Another feature will be 8 motored bogies (out of 10) on the new train compared with 8 out of 12 on the 1973 tube stock. This means better uses of the available adhesion will be possible.
By the way, when a new signalling system does come along similar principles will be used to calculate safe spacing between trains
Finally, 1973 tube stock was always capable of much higher performance than it was ever able to use in service, but was demonstrated when first tested in 1974.
The IRSE published a paper/presentation about safe braking principles for ATO in 2024 which was summarised in a Rail Engineer article:
https://www.railengineer.co.uk/demystifying-the-safe-braking-model/