Lear 60 captain reported an airborne conflict with another aircraft on approach to mwcr.

Narrative:

Our aircraft was cleared for the RNAV 08 approach into mwcr and were inbound to mobix. We queried ATC if they would like a procedure turn after mobix; and the controller indicated he was not expecting a procedure turn at mobix. We passed mobix; turned inbound towards saser; and were level at 1500 ft MSL with the current altimeter setting provided by grand cayman approach (1017 hpa). At this point; we observed a TCAS target 1000 ft above us and converging; moving west to east. This aircraft had been instructed by ATC to hold at 2500 ft. We watched this aircraft on TCAS begin descending directly above us; inbound on what appeared to be a final approach for runway 08; absent of any clearance that we had heard. I queried ATC if this aircraft was supposed to be descending; and ATC indicated that [the aircraft] should be level at 2500 ft and not descending. [The aircraft] then began a climb after reaching 5-600 ft above us (placing them at 2000-2100 ft); with little to no horizontal separation. We did not receive a TCAS TA or RA.

Original NASA ASRS Text

Title: Lear 60 Captain reported an airborne conflict with another aircraft on approach to MWCR.

Narrative: Our aircraft was cleared for the RNAV 08 approach into MWCR and were inbound to MOBIX. We queried ATC if they would like a procedure turn after MOBIX; and the controller indicated he was not expecting a procedure turn at MOBIX. We passed MOBIX; turned inbound towards SASER; and were level at 1500 ft MSL with the current altimeter setting provided by Grand Cayman Approach (1017 hpa). At this point; we observed a TCAS target 1000 ft above us and converging; moving west to east. This aircraft had been instructed by ATC to hold at 2500 ft. We watched this aircraft on TCAS begin descending directly above us; inbound on what appeared to be a final approach for Runway 08; absent of any clearance that we had heard. I queried ATC if this aircraft was supposed to be descending; and ATC indicated that [the aircraft] should be level at 2500 ft and not descending. [The aircraft] then began a climb after reaching 5-600 ft above us (placing them at 2000-2100 ft); with little to no horizontal separation. We did not receive a TCAS TA or 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.

Attributes
ACN	1370555
Time
Date	201607
Local Time Of Day	0601-1200
Place
Locale Reference	MWCR.Airport
State Reference	FO
Environment
Light	Daylight
Aircraft 1
Make Model Name	Learjet 60
Operating Under FAR Part	Part 135
Flight Phase	Initial Approach
Route In Use	Other RNAV Runway 08
Flight Plan	IFR
Aircraft 2
Make Model Name	Challenger CL600
Flight Phase	Initial Approach
Flight Plan	IFR
Person 1
Function	Captain Pilot Flying
Qualification	Flight Crew Air Transport Pilot (ATP)
Events
Anomaly	ATC Issue All Types Conflict Airborne Conflict
Miss Distance	Vertical 500