In the same way as Galarian Farfetch’d in Sword version, Galarian Ponyta is quite difficult to find in Shield.
Where to find Galarian Ponyta?
You have a chance to fall on it in the tall grass of the Glimwood Tangle, just below Ballonlea. Be careful, you won't see it in the tall grass like most Pokémon, you have to wait until an Exclamation Point appears and comes at you.
How to make Ponyta evolve?
There is no specific method to make it evolve. He will become a Galarian Rapidash by passing level 38. It is impossible to find a Galarian Rapidash in the wild. So it's the only way you can get it.