How to trim in level flight when speed increases?
The angle of attack is lower for the faster flying aircraft. More speed means more dynamic pressure, and in order to create the same lift (weight did not change, after all), less angle of attack is needed to create the needed amount of lift.

Now it is important to know that the angle of attack (more precisely, the difference between the actual and the zero-lift angle of attack) on the wing is higher than on the tail if the aircraft is statically stable. If the aircraft accelerates, the relative amount of lift loss on the wing is less than on the tail, because both experience the same reduction in angle of attack. To keep the balance between both the same, this extra lift loss on the tail needs to be compensated by some downward elevator deflection. The center of gravity did not change, and the center of lift must be shifted to the same longitudinal station in order to maintain level flight.

Fun fact: When transitioning from sub- to supersonic speed, the elevator must be trimmed trailing-edge-up, because now the center of pressure moves back on both wing and tail, so their lever arms around the center of gravity change.