Lear 60 captain reported receiving an RA on approach that was contrary to ATC instructions.

Attributes
ACN	1733397
Time
Date	202003
Local Time Of Day	1201-1800
Place
Locale Reference	OPF.Tower
State Reference	FL
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Learjet 60
Operating Under FAR Part	Part 91
Flight Phase	Final Approach
Flight Plan	IFR
Person 1
Function	Captain Pilot Not Flying
Qualification	Flight Crew Instrument Flight Crew Multiengine Flight Crew Air Transport Pilot (ATP) Flight Crew Flight Instructor
Experience	Flight Crew Last 90 Days 70 Flight Crew Total 4200 Flight Crew Type 100
Events
Anomaly	ATC Issue All Types Conflict Airborne Conflict Deviation - Procedural Clearance
Miss Distance	Horizontal 3000 Vertical 0

Narrative:

We were cleared for ILS runway 12 at opf. I was PIC and pm (pilot monitoring) from right seat. Second pilot was PF (pilot flying) from left seat.the following sequence of events occurred:at 2;000 ft. On the approach; opf tower instructed us to climb to 2;500 ft. For traffic. PF initiated a climb. As we began climbing; TCAS issues a resolution advisory (RA) to descend. PF began to lower the nose; as pm notified opf tower that we received the RA. TCAS system changed its indication to command a climb. At the same time; pm acquired the traffic visually and notified PF that traffic was in sight. Traffic passed us on right side with about X mile separation. PF continued approach to normal landing.it would be very useful for ATC to receive live broadcast of TA RA from aircraft; so that controller can avoid issuing instructions that are contrary to TA RA.

Original NASA ASRS Text

Title: Lear 60 Captain reported receiving an RA on approach that was contrary to ATC instructions.

Narrative: We were cleared for ILS Runway 12 at OPF. I was PIC and PM (Pilot Monitoring) from right seat. Second pilot was PF (Pilot Flying) from left seat.The following sequence of events occurred:At 2;000 ft. on the approach; OPF tower instructed us to climb to 2;500 ft. for traffic. PF initiated a climb. As we began climbing; TCAS issues a Resolution Advisory (RA) to descend. PF began to lower the nose; as PM notified OPF Tower that we received the RA. TCAS system changed its indication to command a climb. At the same time; PM acquired the traffic visually and notified PF that traffic was in sight. Traffic passed us on right side with about X mile separation. PF continued approach to normal landing.It would be very useful for ATC to receive live broadcast of TA RA from aircraft; so that controller can avoid issuing instructions that are contrary to TA RA.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.