Time barrier

From Canon Sources
The time barrier was a theoretical barrier in the development of mid-23rd century warp drive. This obstacle was overcome sometime between 2236 and 2254 (between the time of the crash-landing of the SS Columbia on Talos IV and the arrival of the USS Enterprise (NCC-1701), allowing Federation star ships to travel significantly faster than ever before. Episode - (TOS: "The Cage")

Star Trek Origins Time Line
For many years the Star fleet, like many other races of the Alpha & Beta quadrant, try to reach warp 8. Their warp cores, can only archived the necessary energy to create the 8th layer of warp field and reach warp 8 in a very brief time. This enogh to get warp 8 in theory, but some things was falling. When they tried to warp 8, a big delay between the 8th warp field layer creation and warp core max energy peak, was making impossible get warp 8 which these warp cores. Is know the "Time barrier".

So, they new warp cores, and improved warp coils, to reach warp 8... Was necessary that the new warp cores, create a more output of energy and keep the necessary energy enough time to break the "Time barrier".

The Klingons make new Warp 8 core, before of the UFP, based over reverse engineering of capture Hydran ships. But flaws in their design of warp coils, make to get Warp 8. So the Warp 8 barrier was unbeaten yet, except for older warp races, like the Hydrans.

The UFP, make his Warp 8 core from scratch. Their reactor, generate a bit more output energy that the Klingon Warp 8 core, and are in final stages of testing at 2235 in two ships of Arizona class. At same time, the UFP are testing new design of warp coils in the first ships of the Legends class. The Legends class, was designed, originally, for be mainly deep space explorers and break the "Time barrier" which the new warp coils and the new warp 8 core.

Why this barrier
Mainly this barrier, is a false barrier. It come from mainly of bad knowing of warp fields equations. The equations of Cochrane, are only a 75% of the real equation. The unaware parts of the equations, are really showed when the ships reach high warp and can see that was a mistaken in the theoretical speed and the real speed. In the first years of the 23rd century, not was knowed yet it, so when they try to get warp 8, in the true, they not was trying to generate a 8th field in the warp field yet. The true was that they need a lot more of energy to archived it ! In the late mid-23rd century was really begin to discover this bad knowing of the warp fields equations. One of engineers that show this problem and give a first approach of how are the unaware part of the equations, was Montgomery Scott, the Chief Engineer of USS Enterprise (NCC-1701), based over some data obtained of max speed tests of the refitted ship. He used it to show that Trans Warp tech of the  USS Excelsior (NCC-2000) must fail. Which his notes, and more deep warp field studies, was developed the new warp scale around the last years of the 23rd century, that give a more right view of the real speed and energy used, plus show that can reach warp 10, because the 10th warp field layer, always collapses in to 9th warp field in the simulations. This is the main reason of the warp 10 asymptotically speed increase.

So... When is break
When STO launch some chapters, will be show it. We only can conjecture that should be in 2236 or 2237.