Much as I appreciate people would always like to know when the next update will be coming and what it will attempt to address, in practice this is never going to happen. Updates are released when they're judged ready (not always accurately, sadly) and I believe once they've had approval from PlayStation/XBOX and potentially Steam/Origin too.
The Time Trial not working issue for some is a very big deal as it is a core game mode. I use it a lot for practicing myself. I suspect the main reason this hasn't been so prominently been discussed as the tyre related issue is simple that fewer players are affected but as has been covered above it doesn't mean the TT issue is being ignored. Like the rest of you I hope that we'll see a game update soon that addresses both issues.