This official future product roadmap from Acura shows the automaker will launch a new Type S compact sedan in 2022. That will likely be the Integra Type S but they haven't said anything about it yet.
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But there was this trademark for the name "Integra Type S" filed back in August 2021.
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If Acura is still on track to launch the Integra Type S, then it should happen as early as June-July with order books opening soon after that and deliveries around late 2022, for the 2023 model year.

Here's a quick read on why we still haven't heard or seen anything about it yet:

"Acura hasn’t directly stated by word of mouth that there’s an Integra Type-S in the works but if we go back to their new product portfolio chart, we see a “Type-S, new compact sedan” which would validate a Teggy S.

A few people here stated that Acura should’ve led with the Integra Type-S. I’m just going to say why manufacturers don’t lead with lower volume performance trims first.

  1. the 1.5t cars will be the volumes sellers by far.
  2. production ramp up usually deals with regular trims first to get all the production bugs out and to weed out any quality issues that may arise during production.
  3. After that magic production number is reached consistently, then you’ll hear about the performance trims rolling out.
  4. pretty much all manufacturers do it this way as it’s pretty standard across the industry.
  5. The volume sellers pay for the high performance trims.
  6. Also, the majority of the time, the performance trims are still under development and road testing while the base cars are being produced and sold.
  7. Last but not least, high performance trims usually have different development teams vs the regular trims as those engineers always deal with high performance models. I know engineers for the NSX and CTR had a big hand in the TLX-S’ development and probably all Type-S/R cars in general.

Take the 3 Series, Camaro, Corvette, Charger, Challenger, Ferrari etc etc or pretty much any vehicle with multiple tiers of performance trims, the base engined volume sellers are produced first and then the higher performance variants roll out by tier. Honda even does with with the Civic as we got the 1.5t versions first, then the Si debuted a few months after those cars and the the Type-R will be introduced later on."