Wait for federal notice and yes you could if you have already have tps once ... this is according to me btw ....

You don't need to wait for federal notice or re-registration date, you can apply late re-registration any time, before your current status get expired. Start the process asap, it might take 4-5 months to get approved.

See comments below in ( ): - Hi guys needed some suggestions:So, my wife's OPT is ending on July 5th and we didn't re-register for TPS(Failed to maintain existing TPS) last year since TPS was designated to end on June 24th(Based on your answer - reason not to maintain TPS is "It is going to expire in next 12 months anyways"). Now the question is, can we apply for her TPS now (Yes. But with good cause for not maintaining) since it has been extended till Jan 2020? (Interested to re-register now because termination date is extended - Not a good reason) I think already having a different status beyond the TPS end date (Not sure what do you mean by different status) must be a good enough cause for not re-registering. (letter explaining the cause is required for late registration). Also, i plan to apply for her H4 within 60 days after her OPT ends (I would suggest you to apply for her H4 immediately as she needs to give enough time for the process and approval notice) as i am in H1. Please advise!If we can apply for registration,when can/should we apply? (Now) (I think it would be better to apply once the federal register is updated showing how to apply beyond June 24th?) Also, do you guys suggest using a lawyer? (In my opinion, Yes. You need an attorney to handle her TPS case since she missed to maintain it.)Thanks and hoping for responses!

Here comes another kgc....