You'll need to find the data sheet for your LED display or probe it using a diode tester or battery and resistor.
There will be one common cathode pin for each digit and one pin for each digit element. A seven segment display will therefore have seven pins, but there may be one for dots in between. If so, you would expect 8 (anode) + 4 (cathode) pins in total.
To drive a multiplexed display with, say, "1234", you would output a "1" and sink current on the cathode of the first digit. Then output a "2" and sink current on the cathode of the second digit, and so on. Do this fast enough and the number will appear steadily.
If you look at figure 8 in the ICL7107 data sheet, you'll note that it requires a non-multiplexed LED display in this configuration because seven wires are going between each digit and the driver, and there must be a single common cathode. You would need to find a new LED module (or just use four single digit 7-segment displays)