HBOT Access Act of 2021 This bill requires the Department of Veterans Affairs to furnish hyperbaric oxygen therapy through a provider authorized by the Veterans Community Care Program to veterans who have a traumatic brain injury or post-traumatic stress disorder (PTSD), are at high risk of suicide or self-harm, and have used at least two evidence-based treatment options for their condition. Veterans who receive hyperbaric oxygen therapy due to the enactment of this bill must be included in a study on individuals receiving such treatment to determine the efficacy and effectiveness of the treatment for PTSD and traumatic brain injury.