Rule 303,
What you asking for is: Can you use an Australian instructor to carry out one or more functions under Thai law, while in Australia..
That is a matter for the Thai Authority, not CASA.
The aircraft is flying legally in Australia, you are licensed to fly it (anywhere) but you need a check required by the Thai authority?
Or is it that you want to use a foreign registered aircraft to conduct training for a CASA requirement, of a CASA BFR ----- the two are very different things.
In the latter case, the aircraft will have to be entered on the AOC of where you want to do the CASA training ---- this is possible, but the time and cost means that the provisions would normally only be used in an airline scenario.
Tootle pip!!