Complex sentence: It was a subsidiary of Trek Airways (The actual name of the airline was Trek Airways Flitestar, but it operated under the brand name Flitestar) and began operations on October 16,1991 using four new leased Airbus A320-211 aircraft.
Split into simpler sentences: It was a subsidiary of Trek Airways; the actual name of the airline was Trek Airways Flitestar, but it operated under the brand name Flitestar. The airline began operations on 16 October 1991 using four new leased Airbus A320-211 aircraft.