Is a holding pattern required on the Twentynine Palms VOR for RWY 26?
This chart provides two ways to begin the approach. The first is at the TNP VOR, which is labeled as an IAF (Initial Approach Fix). Since a holding pattern is charted, you are required to fly that holding pattern as part of the procedure if you begin at TNP.

The other way to begin the approach is at JEHLI, which is labeled as an IF (Intermediate Fix). The "NoPT" instruction only applies if you start the procedure at JEHLI, as this establishes you on the 255 inbound radial to TNP and no hold is needed.

If a hold or procedure turn is charted, you need to fly that maneuver unless you are coming from an IAF or IF with the "NoPT" instruction (or if ATC clears you "straight in").