if you are currently just a gym member and have no arrangements with the gym to train people there, then getting an understanding with the club is where you have to start. It has nothing to do with lack of respect for the other trainers. People approach us not only for our qualifications but also because they simply like one person better than another.
There are plenty of gyms that will not allow independent trainers to train. Period. And I would strongly urge to resist the temptation to train people under the guise of being ‘workout buddies’.
If the gym allows you to train, they will most certainly want a cut. If they say that it is against their policy, then I would not train the members there. They can approach the club management who may re-consider their position when there is risk to lose a gym membership over it.
Since you already train clients in other locations, you can certainly offer to train them there.