Commercial Fixed Wing
Air Traffic Control Fully Certified
Air Traffic Control Radar 5
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Flight Crew Requested ATC Assistance / Clarification
Procedure
I had just assumed responsibility of the position about a minute prior when the pilot of Aircraft X informed me that they were 'Over HOMAI; what do you want?' The previous controller; still observing the 2-minute overlap; confirmed what she stated in the relief briefing; that Aircraft X had been assigned direct HOMAI; which ties into their flight plan routing of the LNDHY1 STAR into OGG. I responded to the pilot that he should track outbound of HOMAI on the LNDHY1 arrival; which publishes a 204 degree track. The pilots were obviously confused; but began to correct. In the process of doing so; the aircraft may have clipped the boundary of a higher 6;300 ft. MVA. Aircraft X was level at 4;000 ft. in a 3;500 ft. MVA; and would have had no problems remaining so if they were established on the STAR. In an effort to salvage the situation; I asked the pilots if they had the airport in sight for a visual approach. They replied in the affirmative. Then I asked if they had traffic to follow in sight. They replied in the affirmative and I issued the visual approach clearance. The MSAW (Minimum Safe Altitude Warning) did not activate and I did not issue a low altitude alert. The pilots did not question the 'direct HOMAI' clearance they received from the previous controller until they were about a half mile past the fix. If there was any question about their routing; they should've clarified much earlier. But the confusion is not infrequent; and I have had pilots question the routing before. The published STAR clearly shows a 204 degree track after HOMAI on both the visual layout and written description. When I state this fact to querying pilots; the confusion is resolved. But the lack of a fix after HOMAI may cause pilots to ignore the track; or (as some controllers suspect) cause the track to drop out of the FMS when an approach is pre-loaded. My recommendation is for another fix to be added on the 204 degree track after HOMAI; to resolve the confusion; and to help ensure that aircraft don't fly on a free heading toward a higher MVA.My other recommendation is to look into how the LNDHY1 STAR is being programmed into FMS displays; and whether the addition of a (yet to be assigned) approach (e.g. RNAV Z RWY 2 from HOMAI) erases or otherwise obfuscates the 204 degree track outbound of HOMAI.
HCF TRACON Air Traffic Controller reported an aircraft failed to track the STAR resulted in entering a higher MVA.