Should I change gear set to increase gear ratio on old bike (2011 GT Zaskar)?
Your specs link shows a 11-36T  cassette with a double chainring with 39T and 26T.  So your "fast" gear is 39:11.  Assumning 29" wheels with 2.3" tyres, 1 revolution of the crank carries you 


8.9 metres in 39:11 (fast/hard gear)
1.7 metres in 26:36 (easy/slow gear)


Basically you have a mountain bike, and its geared for off-road usage, not too fast.

11 tooth is about as small as you can go at the back reasonably, so increasing the size of your front chainring is about the only option.  It may be untrendy, but a triple chainring with 50/39/26 tooth would give you  10.5 metres travelled in 50:11 which is road bike territory.

You'll need a replacement 3 position shifter and a triple crank.  Your front mech may or may not have enough width to cover all three chainrings.

The other option is to replace both chainrings on your double and slide the front mech up.  This will lose you the lowest hill climbing gears, but sounds like you don't need them.