Local Controller described multiple go-around events resulting from the failure of the TRACON to coordinate an IFR ILS arrival as per LOA.

Narrative

Airport was VFR; active Runway 26R/L; with 2 aircraft in the pattern. The RACD (RADAR) was out of service. When the RACD is out of service; the TRACON is required to coordinate (via phone line) all inbound aircraft on approaches. The TRACON did not coordinate an IFR ILS approach inbound (Aircraft X). Aircraft X called inbound but Local control (LC) did not hear or respond to Aircraft X. Local Control had a helicopter; Aircraft Y; over Runway 26R cleared for the option; when he scanned the approach and saw Aircraft X on short final to Runway 26R. LC sent Aircraft Y around and asked the aircraft on short final to say call sign. Local Control then sent Aircraft X around. If the Local Control had not seen Aircraft X; Aircraft X would have landed with Aircraft Y on the runway. Recommendation; the TRACON Controllers are all very new and need better training on the procedures that are in place in the Letters Of Agreement with other facilities. This situation would not have occurred if the required coordination had been performed.