Hi, let me try
If we consider the airplane as "the system", the law of energy conservation states that the energy at a given instant is: the initial energy plus any energy that came into the system and minus any energy that went out. Energy cannot disappear or be created. Energy is just transfered from one system to another.
In the case of the airplane flying (or a car running), there is energy going out of the system (to the air) due to Drag, friction, etc... In order to maintain the vehicle energy constant, energy from outside must replace the lost energy. This energy comes from the fuel. In this case, I consider fuel as external to the system. But we could consider fuel a part of the system too.
Fuel as external: Airplanes energy state (simplified): potential + kinetic. Energy remains constant as long as there is fuel.
Fuel as internal: Airplanes energy state (simplified): potential + kinetic + fuel energy. In this case, the energy state will decrease continuously until the fuel is depleted. And we have to take into account the engine efficiency, since a large part of the fuel energy will be wasted into the air, too.