You don't need additional +24v power supply.
According to the schematic, during standby, when your microcontroler port pin is at low level, T1 and T2 are locked,
and the C1 is charged at +12v through R1 and R2.
When the port pin goes to high level (+5v), T1 is polarized through R4.
The voltage VCE of T2 decrease near to zero and the voltage across C1 is added with the power supply and applied to the relay (almost +24v).
This is enough to energise the relay until the C1 is discharged by R1.
The relay will receive enough power (current which flow through R1) to keep his contacts closed.
The value of R1 is critical and is strong related to the relay resistance.
In order to find the appropiate value for R1 you must check with a variable power supply, the minimum hold voltage for which the relay is still energized.
If this value is bellow +10v then you can use the schematic. Otherwise it's useless.
On the other hand, the value of R1 must be as higher as possible in order to not discharge quickly the C1 when T1 is driven, or not until the relay is energized.
Hope it will work for you.
Regards,
silvio