Am I doing the gym right - how can I up the ante

Unless your body fat is fairly low already I am sorry, but I think @EarringsandLipstick may be being somewhat optimistic. I spent years doing boxing (which is damned high intensity) plus weighted lunges and kettlebell swings and the like, and made not the vaguest visible difference to my muscle definition even after losing weight to reach a healthy weight. Even now, after two years of properly programmed (by a weight lifting coach) weight training four times a week (with significant increases in weights over the period as I became able to manage it), and losing more fat you can only see the vaguest oblique lines on my abs and no other obvious musculature unless I flex.

Oh don't listen to this! I'm amazed at the nonsense that is posted here at times.

So, yes, if you are talking significant muscle gain, like really getting very muscular, you need to build on your weight lifting, as the other posts said.

BUT that's not what most people want - typically people want muscle definition & you can absolutely get that with HIIT particularly where some weights are incorporated, but they don't have to be heavy or necessarily increase.

It is best done as part of a class, rather than trying to do it individually in a gym.

What that might look like is: weighted lunges, leg raises with a weight, kettlebell swings.

You'll gain toned, defined arms, chest, glutes etc that way.

If you can add in a pure strength & conditioning class, about 1 a week, then that would help & is where you can focus on the heavier weights.

Re flat stomach. Some of that depends on your own natural shape, and of course weight loss. For many women, they'll always have a bit of a tummy. Core work like planks, leg raises, crunches as part of HIIT training help massively.

HIIT and cardio won't build muscle so you need to get a weights programme and follow it.

If you want to increase muscle then you need progressive overload. HIIT and other classes just aren't going to do that. Flatter stomach will need fat loss, for many women it's the last place to go and often not worth the effort (not for me anyway). Bigger bum is going to be barbell hip thrusts and certain squats.

You need to be eating adequate protein (100g a day) spread over 3-4 meals. Unlikely to build much muscle whilst also in a calorie deficit but possible if you're new to lifting.

Have a look at ESG fitness on Instagram. She will also answer all your questions for free if you message her.

Also muscle growth takes time. I've been going consistently for a year (weights only, slowly increasing the load) and I'm finally seeing some biceps I go three times a week, it is enough if you have the right programming.