Are you going to add perlite in to this?
If so, first prepare your medium by adding %20 to %40 perlite in it. You can spray perlite with water to prevent dust during the work.
You may want to flush new compost with PH corrected water before use but it might not be necessary if you will be careful about watering from now on . I can suggest to use rain/deionized/distilled water for one to three watering. You can also mix those with tap water as well.

Now, after preparing the new compost, let the old compost dry out a little but not completely. Like %25 moist to handle easily. After that remove the pot. You must be able to hold the plant from the main stem. Hold the compost from the sides, lightly press and lightly roll in your hands. After that you can hold it from the stem and hit to the floor lightly. Washing out old compost is another alternative. Or you can invent your own way to do this. After old compost cleaned out from the roots (you don't need to clean all. You can do as much as you can, even %50 can be enough.) add some new compost in to bottom of the pot and press lightly (amount is depend on plants height, you can see that), after that add like half or one centimeter more but don't press. Place the roots on to compost, spread around and simultaneously add more soil around and inside the root ball. When you filled it completely, water the pot, let the compost sit and add more from top. Press lightly, water lightly for the last added compost. You're done. Wait until it gets dry for next watering.
You can't spread the roots as best as they were before, don't worry about that, just do your best.

This is just one suggestion from me for you. Before doing this, make a search, wait for other responses here and find the best way for yourself to get success.

Good luck:thumbsup: