Refer to figure.
CAS is IAS corrected for Instrument and Position (Pressure) Error.

CLIMB AT CONSTANT CAS IN ISA ATMOSPHERE

The rapid rise of Mach number (in this case far exceeding MMO) is the reason why high performance aircraft are flown on CAS (or IAS) for the first part of the climb before transferring to a constant Mach number for the rest of the climb.

For a constant CAS as altitude increases, TAS increases, and Mach number increases at a greater rate.

If TAS increases, the climb gradient and rate of climb decrease because kinetic energy is converted into potential energy.

Note: The sum of kinetic energy and potential energy may not exceed the total aircraft energy. The total energy is shared between the need for speed and the need for altitude.