Electronics OR pull chains. The other goes away.
You either control it with the electronic control, OR the pull chains. Not both.
If you want to use an electronic control, then you need to bypass and remove the pull chains, preferably electrically. As user118539 witnessed, weird bad things can happen when you try to use both control methods at once.
That's my fan and switch! When I replaced with a new switch (exactly the same), I couldn't get the switch (fan and light) on the wall and chain (light and blade speed) to work 100%... I got it like 75% and then broke a blade off... (from a deleted "answer")
There simply aren't fan controllers out there designed to properly use both. Effectively this would be a case of rewiring the fan so the chains are alternate switches for the controller's input... but nobody builds a thing like that right now.
Get a matched control module and wall switch.
If there is already a "light switch" in the room that powers the fan, then you can probably get it done without calling an electrician to fish wire. And there ought to be a light switch in the usual place, that is mandatory per the Electrical Code and the Building Codes!
It's possible to have a switch module be the whole kaboodle, but it depends on a very particular wiring scheme (power to the switch, and /3 cable to the fan/light).
For all others, you will need a matched set of control module and wall switch. Fair chance these will be a serial-number-matched set (or have DIP switches to set a code ID) because the manufacturer will want to support independent control of multiple fans.
If power comes to the switch, it is straightforward - you pass power onward to the fan, and the remote communicates wirelessly or with powerline communication (or the red wire as a comm line) to the module. The module sits up in the ceiling above the fan, and takes hot and neutral (and comms), and drives the light and the fan separately
If power comes into the fan, then the wires to the switch are used to extend hot and neutral to the switch (and possibly also comms wire). Other than that, it is much like the above installation.