Help understanding schematic (voltage regulator)
R2, C2, D5, D6, C3, R3. ZD7 is a capacitive dropper type PSU for negative voltage used in op amps. You can place a small DC/DC converter in its place. The main information comes from zener diode, this is the negative voltage value to meet.

Although, it is not clearly why this power supply needs the negative voltage, perhaps some old op amps can't go such low. Imo if you don't need very low voltage to be set on this bench PSU you can get rid of the negative PSU. In such case the resistor R14 has to be changed. Perhaps also changing U3 and U2 with a modern rail to rail op amp won't make much difference even without the negative PSU.

EDIT:

The U3 and U2 are more likely comparators rather than op amps.

EDIT2:

R13 and R14 form a voltage divider. The input voltage 24AC is rectified and you get somewhere around 32VDC. The base-emitter voltage of Q1 gets -0.2V, which means the transistor is in off conduction. Rising the input voltage above certain level the Vbe of Q1 will reach 0.65V and the Q1 will start conduct, thus shutting down the output voltage of the output of the PSU. Kind of input overvoltage protection circuit. You can eliminate the Q1 - not mounted. Then you eliminate the -5V PSU as well. You won't be able to set the output voltage level near 0V, also you won't be able to set the current level at 3mA, only. 

Do not mount components: R2, C2, D5, D6, C3, R3. ZD7, Q1. In place of zener diode ZD7 put a jumper (short = 0 ohm). Test and see, if you are not satisfied, buy a transformer 24VAC.