GND CONFLICT OCCURS BTWN A DEPARTING C172 AND A LNDG BE1900 WHEN TKOF CLRNC WAS CANCELED BUT NOT ACKNOWLEDGED BY C172 AT VPS; FL.

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I WAS THE FLT INSTRUCTOR ON A VFR LCL TRAINING FLT FOR A NAVY INITIAL FLT SCREENING CANDIDATE AT EGLIN AFB; FL. I WAS PLTING A C172N OPERATED BY THE CLUB. AFTER TAXI AND RUN-UP AT RWY 19 AT INTXN N; I INSTRUCTED THE STUDENT TO ASK FOR TKOF CLRNC. I HAD HEARD SOME CHATTER WITH A BEECH 1900 BUT UNSURE OF HIS POS. THE TWR GAVE US CLRNC FOR AN IMMEDIATE TKOF FROM WHICH I INSTRUCTED THE STUDENT TO GET MOVING. MOVING TOWARD THE RWY; I SAW THE BEECH 1900 ON L BASE TO RWY 19 ABOUT 1 MI OUT. AT THE SAME TIME TWR GAVE THE INSTRUCTION 'ACFT X; EXPEDITE YOUR TKOF.' SENSING THE URGENCY; I SAID TO THE STUDENT; 'LET'S GO; LET'S GO.' REALIZING THINGS WERE NOT HAPPENING VERY FAST WITH A 4.5 HR STUDENT PLT; I TOOK THE CTLS AND APPLIED FULL PWR AS WE WERE JUST ROLLING ONTO THE RWY. THERE WAS SOME BACKGND CHATTER WHICH I DIDN'T UNDERSTAND AS I WAS COMMENCING THE ROLL. THEN I HEARD THE BEECH SAY 'THIS ISN'T GOING TO WORK.' A FEW SECONDS LATER; I WAS AIRBORNE; SO I TOLD TWR 'WE ARE OFF THE GND.' AT THAT POINT; TWR INFORMED ME THEY HAD CANCELED MY TKOF CLRNC. I ADVISED THAT I HAD NOT HEARD THE INSTRUCTION POSSIBLY DUE TO COCKPIT TALK. THE BEECH LANDED NORMALLY AND THAT WAS THE END OF THE SIT. BELIEVE THE TWR CLRED US FOR TKOF WITH MINIMAL SPACING FROM ARRIVING ACFT. LOW TIME STUDENT WAS REACTING TOO SLOW FOR THE SIT; TWR GAVE 2 INSTRUCTIONS BOTH OF WHICH WERE TO HURRY. SIT RESULTED IN EXTRA COCKPIT CONVERSATION WHICH COVERED UP THE INSTRUCTION TO CANCEL TKOF. AS INSTRUCTOR; I FELT THE URGENCY TO GET OFF FAST AND I TOOK THAT ACTION.