PHL APCH CTLR EXPERIENCED OPERROR WITH ADJACENT SECTOR TFC DURING LOSS OF COM AND HEARBACK ERROR.

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I WAS WORKING A PC12 THAT DEPARTED PNE S TO OOD; THEN FIRST FIX ON ITS RTE OF FLT. AFTER CLBING PC12 TO 5000 FT; I OBTAINED A POINT FROM THE N DEP SECTOR TO CLB HIM TO 9000 FT FOR OOD. AFTER APPROVAL I THEN CLBED HIM TO 7000 FT; THE HIGHEST ALT OWNED BY PHL APCH IN THE ARD HPASA. AFTER THE ACFT LEFT THIS AREA; I CLBED HIM TO 9000 FT AND SWITCHED HIM TO THE NEXT SECTOR. WITHIN 1 MIN; THE ND CTLR ASKED ME IF HE WAS CLBING. I THEN OBSERVED PC12 STILL AT 7000 FT. AT THIS TIME THE ND CTLR HAD AN AIRLINER LEVEL AT 7000 FT TURNING TOWARDS THE PC12. I ATTEMPTED CONTACT WITH PC12 AND RECEIVED NO REPLY. ND DSNDED THE ACR FLT; BUT STANDARD SEPARATION WAS LOST. CONTACT WITH PC12 WAS ESTABLISHED OVER THE GUARD FREQ AS HE HAD LEFT MY FREQ BUT HAD NOT GONE TO THE CORRECT FREQ. THIS SIT PRIMARILY WOULD HAVE BEEN AVOIDED IF THE ND CTLR HAD PROTECTED FOR THE CLB INSTEAD OF GUESSING THAT THE PC12 WOULD BE OUT OF 7000 FT BY A CERTAIN POINT. I RECEIVED NO READBACK OF THE INSTRUCTION TO CLB AND IF I HAD CAUGHT THIS IMMEDIATELY; THIS INCIDENT MAY HAVE BEEN AVOIDED.