A TRACON Controller reported an aircraft on an instrument approach to a non towered airport initiated a go around due to another IFR aircraft holding for release on the approach end of the runway.

Narrative

I was the Radar Controller on Sector X. There was weather at ZZZ and all throughout Sector X airspace. I had multiple IFR aircraft that needed to be sequenced for the ILS approach. During this; Aircraft Y called me requesting an IFR clearance to ZZZ1. I issued a hold for release clearance and I instructed the pilot to call me back holding short of the runway. The pilot read back that he would call holding short of the runway. Approximately 20 minutes later; the Aircraft Y pilot called me for departure in which I told him to stand by due to traffic inbound on the ILS. The Aircraft X that was inbound on the ILS; called me on frequency to report that they were conducting the missed approach procedure not due to weather but due to an aircraft holding on the runway. I asked the Aircraft Y pilot if he was holding on the runway. He replied yes. Sector X is a very small chunk of airspace that sees a lot of traffic. Traffic at ZZZ has been increasing significantly. This includes business aircraft and local traffic. ZZZ serves as a main airport that practice approaches are being conducted; at all times of the day; mixed with other traffic. According to our NOTAMS; we are required to provide IFR separation to VFR aircraft conducting practice approaches. All of this traffic is making it more difficult to provide the services needed for ZZZ while at the same time controlling traffic and sequencing to other airports. This doesn't even include the VFR aircraft landing and departing that we're not talking to. We need to seriously consider having a Tower at ZZZ to help with workload; efficiency; and most importantly; safety. As it is now; the pilots call us on frequency for clearances and arrival cancellations. When our main and standby frequencies are out of service; and we have to switch to our backup frequencies; which is becoming more common; we cannot hear the pilots on the ground; nor can they hear us. If a pilot wants to talk to us on the ground at ZZZ; they have to call our supervisor or operations manager and relay clearances back and forth which makes it even more difficult and opens us up to more communication errors to the pilot. We have been asking for a Tower for quite some time now; hopefully this incident can be the gateway for that change.