NC Opening Contact detector to drive a NO relay Contact circuit
Try this.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A simple open-collector inverter.


With the switch open Q1 is off and T is allowed to float high.
When the switch closes Q1 is turned on and T is connected to U with, perhaps, a 0.2 V drop between the collector and emitter.