VA Hiring Enhancement Act This bill modifies requirements and procedures related to hiring physicians and applicants for certain other professional positions at the Department of Veterans Affairs (VA). Specifically, the bill negates enforcement of a noncompete agreement that an applicant for such an appointment in the Veterans Health Administration (VHA) has entered into with a non-VA facility or party. As a condition of terminating the noncompete agreement, the applicant must agree to serve at the VHA for one year or until the expiration of the noncompete agreement, whichever is later. Eligibility requirements for a VA physician's appointment are revised to require completion of a residency program rather than an internship. The bill also authorizes the VA to offer a contingent physician's appointment to an individual if the VA anticipates that the individual will, within two years of the offer, complete a residency program leading to board eligibility in a specialty and meet other requirements for the appointment.