Long worms should sometimes generate in areas of sand, carrying a “spice” comestible. If you eat spice, you are granted temporary telepathy, clairvoyance, or both.

Cavemen should have “intrinsic cave awareness” - meaning that they “just know” the layout of the floor they’re on. This could be implemented a couple ways: auto-mapping the rooms on the level but not the corridors when you get within a certain distance; giving you a sort of persistent, limited clairvoyance which maps any walls within a certain radius of you (but not any floors, corridors, or other terrain) every turn, or being able to see walls in line of sight at any distance - but not the floor between you and the wall, if it’s dark.

Ranged divination effects (monster detection, object detection, clairvoyance, maybe telepathy) are suppressed if the level is not mappable.

The spell of clairvoyance grants a few hundred turns of intrinsic clairvoyance when cast at Skilled. This makes it useful for Samurai in particular.

Premonition system: under various conditions (crystal balls, clairvoyance, dreaming while you sleep, the Oracle) you can receive a premonition of something that will appear later in your game (this could be almost anything: a monster, object, dungeon feature, special room, etc) which then has a very high chance of generating subsequently.

If you are a Caveman, you get telepathy or clairvoyance while you are hallucinating.