An apparatus and method are provided for controlling a change in instruction set. The apparatus has processing circuitry arranged to operate in a capability domain comprising capabilities used to constrain operations performed by the processing circuitry. A program counter capability storage element is used to store a program counter capability used by the processing circuitry to determined a program counter value. The processing circuitry is arranged to employ a capability based operation to change the instruction set. In response to execution of at least one type of instruction to load an identified capability into the program counter capability storage element, the processing circuitry is arranged to invoke the capability based operation in order to perform a capability check operation in respect of the identified capability, and to cause the instruction set to be identified by an instruction set identifier field from the identified capability provided the capability check operation is passed.