Do Pals evolve in Palworld?

No. Palworld has no evolution system at all, and this is one of the few questions where a datamine can answer definitively rather than by observation: we extracted all 483 of the game’s data tables and none of them describes an evolution. There is no evolution chain, no evolution item, no level-triggered form change. Searching the English text for “evolve” returns nothing but the Old Revolver and the Marksman Revolver.

Three things get mistaken for it:

• Variants. Many Pals have an elemental variant — Blazehowl and Blazehowl Noct, Vanwyrm and Vanwyrm Cryst. These are separate species with their own Paldex entries, not a later stage. You get one by breeding or catching it, never by levelling.
• Condensing. Feeding duplicates at the Pal Essence Condenser raises a Pal’s stars and stats. It stays the same species.
• Levelling. Stats rise and new active skills unlock, but the Pal never changes form.