How to execute member-function-pointer with a smart pointer object?

First of all, your shown code and the error message does not match. For the given code you should be getting (from clang) following error message

error: left hand operand to .* must be a class compatible with the right hand operand, but is 'std::unique_ptr<Registers>'    
   (registerList.*setRegister)();
            ^

This can be solved by dereferencing the pointer(like in @Caleth's answer):

((*registerList).*setRegister)();

---

Now the error message that was shown in the question: no match for ‘operator->* should be coming when you would have tried the following syntax.(Minimal reproducible code)

(registerList->*setRegister)();

This is because smart pointers do not have the pointer-to-member access operator defined in the standard. Therefore, you need to go for dereferencing the smart pointer via operator* or by member function std::unique_ptr::get, and call the member function.

Using the member std::unique_ptr::get the correct syntax would be (See the live demo online)

(registerList.get()->*setRegister)()

---

That being said, if you have access to c++17 use unified version of function invoker std::invoke to invoke the member function with the respective instance, by which you can forget about the (maybe)complicated syntax for operator->*.

Your code has a couple of issues too:

• The member function pointer type in your opcodeLdWordRegister is wrong.It should have been

  return_type(Class_name::* variable_name)(/*parameters_types, if any*/)
  

  Following is the fixed version.

  #include <functional>  // std::invoke
  
  void opcodeLdWordRegister(uint16_t(Registers:: * setRegister)())
  //                                 ^^^^^^^^^^^^^^^^^^^^^^^^^ >>> correct syntax
  {   
      std::invoke(setRegister, registerList);
      //          ^^^^^^^^^^^                 member function
      //                       ^^^^^^^^^^^^   instance
   }
  

• Secondly, dereferencing of the uninitialised registerList pointer will cause UB.

Following is the demonstrative minimal complete example for the case: (See the live demo online)

#include <iostream>
#include <functional>  // std::invoke
#include <memory>      // std::unique_ptr

class Registers
{
   uint16_t sp{2};        // member initialized with 2
public:
   uint16_t getSP() const // function can be marked const as it does not alter the member
   {
      return this->sp;
   }
};

auto registerList = std::make_unique<Registers>(); // initialized the pointer with default object

void opcodeLdWordRegister(uint16_t(Registers::*setRegister)() const)
//                                 ^^^^^^^^^^^^^^^^^^^^^^^^^  correct syntax
{
   std::cout << std::invoke(setRegister, registerList);
}

int main()
{
   opcodeLdWordRegister(&Registers::getSP);
   return 0;
}

Output:

2

If you don't have std::invoke, you can still do what it would do, which is to dereference the (unique) pointer in the call site.

((*registerList).*setRegister)();