Thank you all for your replies. My confusion arises because I saw footage of the barber pole on the airspeed indicator increasing as the Concorde climbed. At first I thought the airspeed indicator was unusually showing TAS, which would’ve explained what I saw. However, I believe this was not the case.
I quote this from what I read on another forum: “Firstly, when below the tropopause, climb at a constant IAS and as the OAT fell her Mach number would increase. Most subsonic aircraft do this anyway, climbing at a constant IAS (though not generally VMO!) until reaching their desired Mach number, when they transition to a constant Mach number for the rest of the climb.
Secondly, at or above the tropopause, the OAT would (in theory) remain constant at -56.5°C and would not fall further as she climbed, so this first technique would no longer work. Now, in order to increase her Mach number, Concorde had to climb and utilise the fact that her VMO increased steadily, by 10kts per 1,000 ft above the tropopause, and so by climbing higher she could now gradually increase her IAS, and thus her Mach number.
Thirdly, at around FL440, Concorde’s VMO stopped increasing and stayed at 530 kts IAS for the rest of the cruise/climb. With no further IAS increase possible, and no OAT decrease likely, the only way now to increase her Mach number was for her to climb at 530 kts IAS and utilise the fact that during a climb at fixed IAS, as the ambient air density decreases, TAS, and hence Mach number, will both rise.”
I am confused on the fact how the VMO was able to increase as an IAS/CAS with altitude.