PLT IS CLRED TO LAND RWY 24 AT ROA AND ACFT Y IS CLRED TO TAKE OFF PRIOR TO THE ARR OF ACFT X. ACFT X GOES AROUND AND HAS NMAC WITH ACFT Y.

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RETURNING TO ROA ARPT FROM THE NE; WE WERE CLRED TO LAND ON RWY 24 APPROX 8 MI NE OF THE FIELD. WHILE SETTING UP FOR THE LNDG; ANOTHER ACFT ON THE GND CALLED FOR TKOF CLRNC FROM THE INTXN OF RWY 24 AND TXWY N. THE CTLR GAVE THE OTHER PLANE DISTANCE REMAINING FROM THE TXWY AND ADVISED HIM THAT FULL LENGTH WAS AVAILABLE. THE CTLR THEN CLRED THE ACFT FOR TKOF FROM TXWY N. I HEARD SOMEONE IN THE BACKGND OF THE TWR YELL 'NO' WHEN THE CTLR GAVE THE CLRNC. I IMMEDIATELY TOOK THE PLANE FROM MY STUDENT AND CALLED THAT WE WERE ON A 1/4 MI FINAL AND THAT WE WERE EXECUTING A GAR. THE CTLR BECAME FLUSTERED AND INSTRUCTED US TO BREAK OUR GAR TO THE L OF THE RWY AND TRIED TO CANCEL THE TKOF CLRNC FOR THE OTHER ACFT. THE OTHER ACFT HAD ALREADY BECAME AIRBORNE; WAS IN A CLB AND DRIFTING TOWARDS US. THIS WAS PINCHING US BTWN THE OTHER PLANE AND THE CTL TWR. I MADE A BANKED TURN AROUND THE CTL TWR AND ANNOUNCED THAT I WAS ENTERING THE L DOWNWIND TO RWY 24. AT THIS POINT THE CTLR FINALLY RECEIVED A RESPONSE FROM THE OTHER PLANE WHO STATED THAT HE HAD EXPERIENCED INTERFERENCE ON HIS RADIO AND HAD MISSED THE PREVIOUS CALLS. I FLEW THE PATTERN BACK TO THE RWY AND MADE A LNDG WITHOUT FURTHER INCIDENT.