In terms of time scales for the big things:
Ghost Train: October 2014
Swarm: February 2011
Saw: November 2007
Stealth: November 2004
Nemesis Inferno: April 2001
Colossus: June 2000
So the last 3 coasters (and last 4 major investments) have had plans submitted at most 18 months before the planned opening date. Inferno and Colossus are stranger ones for a variety of reasons (will explain at the end for anyone interested).
The thing with Stealth, Saw and Swarm though is they were all approved after being mentioned in the park's MTDP at the time. In other words, there was already a level of "pre-approval" to those rides existed, which makes the application process a bit smoother and easier.
Ghost Train technically wasn't mentioned in any MTDP, but they conditions of its construction did not break the MTDP. So even though the park had to submit a full planning application, it wasn't exactly taxing.
With any potential new coaster, there's no current MTDP and no level of pre-approval. So that creates an unknown for the application - moreso with locals (since the park will still be having some discussions with the council authorities prior to submitting plans). This could mean the approval process takes a bit longer, or is a bit more complex. Though, I won't lie, I wouldn't know all the ins and outs there.
So in theory, 2023 could still be on the cards. But at the same time, I'd be surprised if Thorpe and Chessington opened big things at the same time. And 2024 seems to be a rumour floating around more.
Equally, depending on the size of the project (and the scale of any deconstruction and groundworks that need to take place), it could take a while.
In any case, if a 2024 coaster does happen, I'd expect to see an application appear sometime around next summer or later.
Side note about Inferno and Colossus.
-One original plan for Colossus was to be a Premier Launch Coaster, which would have opened in 2001. The park submitted plans for that in December 1999, which were approved. However, they changed their minds, and eventually ended up with Colossus, and the plans were submitted in June 2000, by which point a 2001 opening wouldn't have been feasible in any way.
-Of course, there was the Thorpe Park Fire in 2000, which affected old rides in Inferno's location. One early plan was to get in a Vekoma SLC on the cheap, and quickly build it, so it could open in summer 2001. Another option was for a Rock n Roller Coaster clone. A plan was submitted in September 2000 for this summer 2001 coaster, but quickly withdrawn.
I assume the park opted to go for quality over a quick fix in this case, and low and behold, Inferno was born. Good choice in my eyes too.