We present a study of the distribution of X-ray AGN in a representative sample of 26 massive clusters at 0.15 { < } z { < } 0.30 , combining Chandra observations sensitive to X-ray point sources of luminosity L _ { X } { \sim } 10 ^ { 42 } erg s ^ { -1 } at the cluster redshift with extensive and highly complete spectroscopy of cluster members down to { \sim } { M } ^ { * } _ { K } { + } 2 . In total we identify 48 X-ray AGN among the cluster members , with luminosities 2 { \times } 10 ^ { 41 } -1 { \times } 10 ^ { 44 } erg s ^ { -1 } . Based on these identifications , we estimate that 0.73 { \pm } 0.14 % of cluster galaxies brighter than M _ { K } { = } { - } 23.1 ( M _ { K } ^ { * } { + } 1.5 ) host an X-ray AGN with L _ { X } { > } 10 ^ { 42 } erg s ^ { -1 } . In the stacked caustic diagram that shows ( v _ { los } { - } { < } v { > } ) / \sigma _ { v } versus r _ { proj } / r _ { 500 } , the X-ray AGN appear to preferentially lie along the caustics , suggestive of an infalling population . They also appear to avoid the region with lowest cluster-centric radii and relative velocities ( r _ { proj } { < } 0.4 r _ { 500 } ; |v { - } { < } v { > } | / \sigma _ { v } { < } 0.8 ) , which is dominated by the virialized population of galaxies accreted earliest into the clusters . The line-of-sight velocity histogram of the X-ray AGN shows a relatively flat distribution , and is inconsistent with the Gaussian distribution expected for a virialized population at 98.9 % confidence . Moreover the velocity dispersion of the 48 X-ray AGN is 1.51 { \times } that of the overall cluster population , which is consistent with the \sqrt { 2 } ratio expected by simple energetic arguments when comparing infalling versus virialized populations . This kinematic segregation is significant at the 4.66- \sigma level . When splitting the X-ray AGN sample into two according to X-ray or infrared ( IR ) luminosity , both X-ray bright ( L _ { X } { > } 10 ^ { 42 } ) and IR-bright ( L _ { TIR } { > } 2 { \times } 10 ^ { 10 } L _ { \odot } ) sub-samples show higher velocity dispersions than their X-ray dim and IR-dim counterparts at { > } 2 { \sigma } significance . This is consistent with the nuclear activity responsible for the X-ray and IR emission being slowly shut down as the host galaxies are accreted into the cluster . Overall our results provide the strongest observational evidence to date that X-ray AGN found in massive clusters are an infalling population , and that the cluster environment very effectively suppresses radiatively-efficient nuclear activity in its member galaxies . These results are consistent with the view that for galaxies to host an X-ray AGN they should be the central galaxy within their dark matter halo and have a ready supply of cold gas .