It was previously showing on screen but now I can't find it, even when the object with the subdivision surface modifier is selected. I have managed to apply a modifier via searching the modifier but I'm unable to modify its properties .
2 Answers
you need to select an object that can have modifiers applyed onto it, and then on the right on the properties panel under the wrench tab.
You have accidentally pinned the Properties Editor when you had a different item selected. So now, even though you clearly have a mesh selected, you don't see the Modifiers, as the properties editor shows you information about something else.
Click the PIN needle to unpin the editor, then everything should be back to normal: