transistor biased but not conduct
Your circuit is badly designed in several regards.
As a first point, you have a segment current of about 60 mA, so the total anode current can be as high as 420 mA with 7 segments on. A1015 has a maximal collector current of 150 mA and a rather low guaranteed current gain at high currents.
So you should start by choosing a suitable PNP transistor and determine the base current, that has to be provided with worst case transistor specs. You should expect e.g. 5 or 10 mA, depending on the transistor. A PNP darlington could be used to reduce the base current below 1 mA.
Then, design a level converter, that is able to drive this current, possibly with varying supply voltages. If the supply known stable, the suggested Z-Diode level shift can work, but there are better ways with similar effort, I think. I suggest an auxilary NPN transistor driven from the uP (through a base series resistor) as a level shifter.