PNP transistor constant current source
I would like to know if it is necessary to add a base resistor to the Q1 transistor

No.  The circuit looks like a 12-to-13 mA constant current source, so D1 has a constant current despite variations in the 42 V supply and its downstream load.  As such, circuit action will keep the Q1 base current well below 1 mA.
A Q1 base resistor would protect Q1 in the event that both Q2 and D1 dead-shorted, but that resistor also reduces the &quot;constant-ness&quot; of the constant current circuit.  Even though the Q1 base current is very small, it does vary with changes in the 42 V source because its gain curve is not flat.  This variation in base current will appear as a variation in the voltage across the base resistor, which adds to the Q1 Vbe voltage that is critical to the circuit's operation.  IOW, a base resistor will make the output current vary more with changes in the source and/or load than it would without the resistor.