IFR airplanes are expected to coordinate with each other if two airplanes arrive to shoot an approach at the same time in uncontrolled airspace. Whomever arrives first is going to be announcing their intentions per the reporting requirements, and someone following, if they are that close behind and could have a conflict, will have to figure out an appropriate way to delay their arrival, such as holding at a fix. There's nobody to tell you what to do, so you just use common sense.
The key thing is the requirements are to report your arrival, and your progress at specific stages in the approach, and if you are sharing airspace with another IFR flight arriving at the same time (pretty rare), you coordinate your actions to stay out of each other's way in the same way you would if you were VFR.