We present an analysis of the X-ray active galactic nucleus (AGN) population in a sample of seven massive galaxy clusters in the redshift range 0.35<z<0.45. We utilize high-quality Chandra X-ray imaging to robustly identify AGN and precisely determine cluster masses and centroids. Follow-up VIsible Multi-Object Spectrograph optical spectroscopy allows us to determine which AGN are cluster members. Studying the subset of AGN with 0.5-8keV luminosities >6.8x10^42^erg/s, within r~<2r_500_ (approximately the virial radius), we find that the cluster AGN space density scales with cluster mass as ~M^(-2.0+0.8-0.9)^. This result rules out zero mass dependence of the cluster X-ray AGN space density at the 2.5{sigma} level. We compare our cluster X-ray AGN sample to a control field with identical selection and find that the cluster AGN fraction is significantly suppressed relative to the field when considering the brightest galaxies with V<21.5. For fainter galaxies, this difference is not present. Comparing the X-ray hardness ratios of cluster member AGN to those in the control field, we find no evidence for enhanced X-ray obscuration of cluster member AGN. Lastly, we see tentative evidence that disturbed cluster environments may contribute to enhanced AGN activity.