would I use transistors, diodes or something else
Seeing LEDs are diodes, we'll go with a yes to diodes.
Transistors? Very likely if you want to use the clock's LED driver.
You would configure the transistors as logic gates.
The "something else" could be resistors.
Your clock would need to be a digital clock with 7 segment digits.
You would need to know the pinout for the 7 segment LED driver.
You would need to know the driver's current and voltage for each segment.
You would drive the logic gates with with two of the clock's segments.
Build a logic table for the segments when the hour digit is a three, six, or nine. You need a logic combination that will have a unique output for each of these three digits. The outputs of the logic gates would drive another transistor that turns the LEDs off and on. OH! Look, more diodes!
It's not going to be easy to use the drivers in the clock.
Your best bet would be to use a microcontroller with a realtime clock to drive the red, yellow, and green LEDs. It will work with any type of clock, analog or digital.