CE560 FO INBOUND TO RWY 32 AT ZZZ REPORTS OPPOSITE DIRECTION DEPARTURE THAT CAUSES TCAS ALERT. DEPARTING LEAR FAILED TO TURN AFTER TKOF AS INSTRUCTED.

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WE WERE INBOUND. ZZZ APCH WAS THE CTLING AGENCY. THE ACTIVE RWY WAS RWY 14 WHEN WE LEFT A RADAR VECTORED HOLD. WE RECEIVED VECTORS FOR THE RNAV/GPS APCH TO RWY 14. THEN WE RECEIVED NEW VECTORS DUE TO A RWY SWITCH TO RWY 32. AFTER RECEIVING VECTORS FOR THE RNAV/GPS APCH TO RWY 32 WE WERE CLRED FOR THE APCH. WE RECEIVED NOTIFICATION THAT THE ACTIVE RWY WAS SWITCHED BACK TO RWY 14 BUT WE WERE TO CONTINUE THE APCH TO RWY 32. SO THE ACTIVE RWY WAS SWITCHED 2 TIMES (FROM RWY 14 TO RWY 32 AND BACK TO RWY 14). CONTINUING INBOUND ON THE APCH TO RWY 32; ANOTHER ACFT WAS RELEASED FOR TKOF ON RWY 14. THE OTHER ACFT SHOWED UP ON THE TCAS AS BEING 12 O'CLOCK POS AND 3 MI OUT. HE CONTINUED TO CLB IN OUR DIRECTION UNTIL WE RECEIVED A TFC ALERT AND HE SHOWED LESS THAN 2 MI AND -200 FT AND CLBING. WE INITIATED A TURN TO THE L AND RECEIVED A NEW RADAR VECTOR OF 270 DEGS FROM ZZZ APCH. THE PROB WAS CAUSED BY AN ACFT BEING RELEASED ON THE OPPOSITE DIRECTION RWY WHILE AN IFR ACFT CLRED FOR THE APCH WAS INBOUND TO THE RWY. ACCORDING TO APCH CTL THE APCHING (LEARJET) ACFT DID NOT FOLLOW INSTRUCTIONS TO CLB OUT ON AN EASTERLY DIRECTION. IN ADDITION: THE ACTIVE RWY WAS SWITCHED 2 TIMES CAUSING ACFT TO LAND AND TAKE OFF IN BOTH DIRECTIONS WITH LOW IFR MINIMUMS. THE WIND DIRECTION AND SPD WERE APPROX FROM THE NE (BTWN 030 AND 060) AT 5-6 KTS. IN THIS CASE THE ACTIVE RWY DID NOT NEED TO BE SWITCHED 2 TIMES CAUSING OPPOSITE DIRECTION TFC. CORRECTION OF THE SITUATION OR PREVENTION OF RECURRENCE COULD BE REACHED WITH MORE CTL OF LNDG AND DEPARTING ACFT; NOT ALLOWING ACFT TO DEPART THE RWY WHEN ANOTHER ACFT IS INBOUND ON THE OPPOSITE DIRECTION RWY.