Common workflow is to make a copy(shift+D) before applying the mirror modifier. Then move the copy with the modifier to a collection and uncheck the check box next to that collection. This removes it from the viewport and from being rendered. If you need to make a change then you check it and then make the change to the one with the modifier. Duplicate it and apply the modifier. Then in the data/mesh tab of properties editor look at the name at the top. Select the object you want to switch with this new version and goto the data/mesh tab of properties and click in the name area and either type the name from the new version or scroll thru the list and select it. Note: if you have multiple objects select hold alt down while you click in the name field so that Blender knows to change all selected objects. Then delete that extra copy and uncheck the collection again. Side note: having multiple objects pointing to the same data is instancing. If you have instances/linked duplicate there will be a number next to the name in the data tab. You can select a linked duplicate and make it a full duplicate(aka complete copy) by click on the number next to the name in the data tab.
