You need a little C++ to get things going. I’m going to use a simpler structure to make the answer more readable. In your binding code:

#include <pybind11/pybind11.h>

#include <functional>
#include <string>

namespace py = pybind11;

struct Foo
{
    int i;
    float f;
    std::string s;
};

struct Bar
{
    std::function<bool(const Foo &foo)> python_handler;
    std::function<bool(const Foo *foo)> cxx_handler;

    Bar()
    {
        cxx_handler = [this](const Foo *foo) { return python_handler(*foo); };
    }
};

PYBIND11_MODULE(example, m)
{
    py::class_<Foo>(m, "Foo")  //
        .def_readwrite("i", &Foo::i)
        .def_readwrite("f", &Foo::f)
        .def_readwrite("s", &Foo::i);

    py::class_<Bar>(m, "Bar")  //
        .def_readwrite("handler", &Bar::python_handler);
}

Here, Foo is the object that is passed to the callback, and Bar is the object that needs its callback function set. Since you use pointers, I have wrapped the python_handler function with cxx_handler that is meant to be used in C++, and converted the pointer to reference.

To be complete, I’ll give a possible example of usage of the module here:

import module.example as impl

class Bar:
    def __init__(self):
        self.bar = impl.Bar()
        self.bar.handler = self.handler
        
    def handler(self, foo):
        print(foo)
        return True

I have used this structure successfully in one of my projects. I don’t know how you want to proceed, but perhaps if you don’t want to change your original structure you can write wrapper classes upon them that use the given structure.

Update:

I thought that you controlled the structure when I wrote the answer above (I’ll keep it for anyone who needs it). If you have a single cli instance, you can do something like:

using Handler = std::function<bool(std::string, int, int)>;

Handler handler;

bool cb(ClientInterface *client, const Member *member, int member_num)
{
    return handler(std::string(member->x), member->y, member_num);
}

// We have created cli somehow

// cli->set_callback(cb);

// cli->join();

PYBIND11_MODULE(example, m)
{
    m.def("set_callback", [](Handler h) { handler = h; });
}

If you have multiple ClientInterface instances, you can map ClientInterface pointers to handlers and call the appropriate handler in the cb function based on given ClientInterface pointer.

Note: I haven’t tested the above with a python script but it should work.

Another Update

If you want to handle multiple instances, the code can roughly look like this:

using Handler = std::function<bool(std::string, int, int)>;

std::map<ClientInterface *, handler> map;

bool cb(ClientInterface *client, const Member *member, int member_num)
{
    // Check if <client> instance exists in map
    return map[client](std::string(member->x), member->y, member_num);
}

PYBIND11_MODULE(example, m)
{
    m.def("set_callback", [](int clientid, Handler h) 
    {
        // Somehow map <clientid> to <client> pointer
        map[client] = h;
    });
}

Note that this isn’t a runnable code and you need to complete it.