Light Transport
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Conflict Airborne Conflict
Air Traffic Control Provided Assistance; Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Airspace Structure; Procedure
We received a TCAS RA while being vectored for the visual approach to Runway 36 at PIE. We were flying an assigned heading of 180 degrees and assigned speed of 170 knots when Tampa Approach advised us of traffic at our 12 o'clock and below. I was able to see the traffic on TCAS; but unable to visually acquire it. A moment later we received a TCAS RA to climb. We followed the advisory and climbed 300-400 feet at which time we received another advisory that we were clear of the conflict. I immediately advised ATC of the TCAS RA at which time the Controller instructed us to descend back to 3;000 feet. Tampa Approach had no further comment. I believe the conflict was caused by a VFR aircraft that was 500 feet below us; underneath the Class B and may have initiated a climb.
Light Transport aircraft First Officer reported receiving a TCAS RA during visual approach to Runway 36 to PIE airport.   The TCAS RA was followed and was reportedly triggered by a VFR aircraft transiting below the TPA Class B airspace.