Tower Controller reported an aircraft did not turn to assigned heading on departure.

Narrative

As combined Ground; Local; Flight Data; Clearance Delivery in a TRACAB configuration; Aircraft X requested IFR Clearance to Healy River. Aircraft X as issued taxi instructions and was cleared to Healy River via direct; issued a right turn heading 038; maintain six thousand; issued departure frequency; and issued a squawk code. Aircraft X read back cleared direct; maintain six thousand; an incorrect departure frequency; and the squawk. Aircraft X was issued the correct departure frequency. Aircraft X taxied to Runway 2R and was issued a take off clearance. I was informed that the pilot did not turn right heading 038 as instructed and had to be corrected by departure control; and was also issued a low altitude alert by departure. With an apparent influx of newer pilots to established companies on the airport; I should reiterate the heading to be flown and ensure a correct readback when issuing clearances. While not required to be read back; ensuring that pilots know what is expected of them could prevent recurrent issues.