We present new Australia Telescope Compact Array (ATCA) observations of the young (<102 years) radio galaxy PKS B1718–649. We study the morphology and the kinematics of the neutral hydrogen (H I) disk (MH I = 1.1 × 1010M⊙, radius ~30 kpc). In particular, we focus on analyzing the cold gas in relation to the triggering of the nuclear activity. The asymmetries at the edges of the disk date the last interaction with a companion to more than 1 Gyr ago. The tilted-ring model of the H I disk shows that this event may have formed the disk as we see it now, but that it may not have been responsible for triggering the AGN. The long timescales of the interaction are incompatible with the short ones of the radio activity. In absorption, we identify two clouds with radial motions that may represent a population that could be involved in triggering the radio activity. We argue that PKS B1718–649 may belong to a family of young low-excitation radio AGN where, rather than through a gas-rich merger, the active nuclei (AGN) are triggered by local mechanisms such as accretion of small gas clouds.