Is there such thing?
No, but that shouldn’t stop you from creating your own custom hotkey.
I noticed that there is a command for adding subdivision modifier(Ctrl+1 ; Ctrl+5) and it was “object.subdivision_set”.
So I tried to add “object.mirror_set” but that did not work. I have no idea what else to put there.
There is an easier way: Hover your mouse over the Mirror Modifier button in the Add Modifier panel and RIGHT-click. A small menu will pop up which will include an option to Add Shortcut.
This right-click option exists for most buttons in Blender, it is an easy way to add shortcuts to things!