I update my ipod touch with version 2.1 compatible with ios 7 and I can acces to TSgold

With 2.1 you either have a 1st generation or a 2nd generation. Both cannot run iOS 7 (they are way too old)

The 1G can go to 3.1.3 and the 2G to 4.2.1.

And please provide a link to your TSGold app, i cannot find it in the App Store. Thanks

I suspect y have a 1G iPod

Connect the iPod to your computer and update via iTunes as far as your iPod model allows

iOS: How to update your iPhone, iPad, or iPod touch

A 1G iPod can go to iOS 2.2 via iTunes and iOS 3.1.3 via

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)

To more easily find compatible apps:

iOSSearch - search the iTunes store for compatible apps.

Apple Club - filter apps by iOS version.