I broadly agree with the previous, but you need to separate a few things.
First, you will *in principle* need a visa to go to the US. This applies to all foreign nationals visiting the US. However, if you are a citizen of some 30-odd "western" states (full list somewhere on the web) and if you satisfy a few other criteria, you can apply to gain entry under the Visa Waiver Programme (VWP). Which is what it says on the tin: The ability to enter the US without a formal visa.
One of the criteria for the VWP is that your primary reason for visiting the US is short-term business or tourism. If your primary reason is something else, then you would not be eligible for the VWP and would need to obtain a proper visa.
So if you are exclusively going to the US to perform the flight training to obtain or reactivate some sort of pilots license, then it can be argued that you do need an M-1 visa, and are not eligible for entry under the VWP. It doesn't make a lot of sense to have that discussion here, since it's ultimately the friendly official at the airport who decides what applies. But it is pretty much established that you do need an M-1 visa for ab-initio flight training, and it is also pretty much established that you do not need an M-1 visa if all the training you're going to do is the BFR to make an existing "standalone" FAA PPL or freshly issued "based on" FAA PPL valid - especially if you plan a flying holiday after the BFR. Since your case sits somewhere in the middle of those extremities, I suggest you do a little further research into this, and maybe even get a written opinion from DHS as to your case.
Secondly, TSA clearance. You need TSA clearance for your initial FAA airmans certificate, and for any training that substantially enhances your ability to fly a large airliner (into a building): IR, ME and such. TSA clearance is not required for things like tailwheel and floatplane endorsements. Furthermore, TSA clearance is NOT required if you want to obtain an FAA "based on" PPL.
So if all you want is to revalidate (or whatever it's called) your existing FAA CPL/ME/IR, then TSA clearance is not required. However, should you want to use the opportunity to add something to that rating, then TSA clearance might be required. But again, to be on the safe side, you can always get a written opinion from the TSA.