I posted THIS LINK in my previous answer. You will find reference to various options under Environmental Protection laws.
The critical issue here is that a DA permitting them to run a gym does not necessarily imply that they are allowed to disturb your peaceful enjoyment of your home.
A gym could, for instance, hold one of those spin classes where everyone wears headphones and there is no noise. Or it could run yoga or pilates classes.
Noise is not an essential element of a gym and unless it specifies that noise is allowed in the DA, it shouldn’t make any difference.
FYI, here is how the government defines offensive noise (emphasis mine):
What is offensive noise?
The definition of offensive noise in the POEO Act is noise:
(a) that, by reason of its level, nature, character or quality, or the time at which it is made, or any other circumstances:
(i) is harmful to (or is likely to be harmful to) a person who is outside the premises from which it is emitted, or
(ii) interferes unreasonably with (or is likely to interfere unreasonably with) the comfort or repose of a person who is outside the premises from which it is emitted, or
(b) that is of a level, nature, character or quality prescribed by the regulations or that is made at a time, or in other circumstances, prescribed by the regulations.
For further information about what constitutes offensive noise see the Noise Guide for Local Government.