Do you have some good tips how to have stronger grip in the saddle? Some fitness excercise?

Try full seat breeches! Do squats nightly, use no stirrups often, and when you do use them keep them long!

Squats are good

Lovely thank you very much!

The main muscle that keeps you in your saddle are your upper/inner thigh muscles so just work with your horse sturriupless sitting trot and work to move with your horse as much as you can, I do my sturripless work right after a ride as we cool down and I let my horse stretch out while I do it so he can relax while I work on myself

Try working without stirrups?