When sprinting in the game, my stamina depletes and I have to wait for it to regenerate. Is there a way that I can run 'forever'?
Yes, actually there is.
It's worth turning on the Stamina Bar display in the options for this technique.
If you hold the run button down (PS4 Circle in Control Set A), for a whole stamina bar, then just as it's about to empty, let go of the run button, and immediately hold it down again.
When done correctly, Noctis will flash green, do a little 'shimmy dash' and your stamina bar will refill.
There's some buffs earned with Ignis cooking that could give you infinite stamina:
- Sizzling Humongo-Steak
- Smoked Dualhorn Shank
- Thick and Juicy Steak
- Smoked Behemoth
- Royal Round Paella
- Crispy Cheese Pizza
Find the location in the source link below.
It should be noted that you can also gain stamina back by sprinting directly towards a low fence/railing, and Noctis will vault over them and recover some stamina (approximately half of the maximum amount of the bar).
Certain rocks (roughly waist height) can also be vaulted over, or stamina can be regained by sprinting directly towards a brick/stone wall, which causes Noctis to kick off it.
These techniques can be used in conjunction with the letting go of the sprint button when the bar is low (there aren't always things available to vault over).
A small amount of stamina is also recovered when picking up items/ore/food ingredients.
As the other answers are totally correct and helpful, one additional way to sprint without running out of stamina is to wear the Royal Raiment outfit with no jacket. This outfit is only available as a pre-order bonus, or as an item in the collector edition of the game, but it gives you +30% to Magic, and the most important there, infinite stamina. So if you don't really care about additional stats from clothes and just want to run indefinitely, you can wear this outfit.