All my '80 TR8 has is an oil low-pressure light--no gauge came on these cars. I checked the wiring diagram in my Haynes manual for a 1980 carburetted USA model (which I assume applies to the TR7 and TR8). The oil low-pressure light has one white/brown wire that attaches to the oil-pressure sending unit. The sending unit has 3 wires, as you said. The one already mentioned goes to the light, one "slate"/white wire goes to ignition, and one white/purple wire goes to the anti-run-on valve.
How many wires does your new gauge have? Maybe the sending unit is designed to connect only to the gauge and the gauge connects to the ignition. But then how does the sending unit get its power?
When you figure it out, let us all know. I would like to replace my clock with an oil pressure gauge since the clock doesn't work and I never use the clock in a car anyway.