Parenting the rig to the character will not do anything except make your rig object follow your character object if moved arround.
If you want your character object to be deformed by your rig, you need to parent your character object to your rig with an armature deform.
To do this, select your model, then your armature, hit ⎈ CtrlP to open the Set Parent To
menu, and any of the Armature Deform's three sub-options :

Once it's done, depending the option you chose, your rig might already be able to move your character, but it's very rough, parts might be poorly assigned to bones, ... So you will probably have to edit this yourself.
If you chose Empty Groups or automatic weights (which I recommend for new users), you will have to go in weight paint mode and tweak.
There are a lot of tutorials and manuals about this process, so I invite you to find a nice one for you and see how it goes.