Hi,
I suspect that the timeclock energises the coil of a contactor. The contractor will contain a number of switching contacts which close (switch on) when the coil is energised.
One side of these contacts will be fed from circuit breaker(s) or fuse(s) in the distribution board. The outgoing side will supply the external lighting. It may be that both line and neutral are switched by the contactor.
To add another circuit, you'll probably need another contactor. Loop the coil feed from the existing contactor to also feed the coil of your new contactor so the both operate together. Then run a new lighting circuit through the new contactor to the new lights.
LED's can have quite a high start up current, so get s contactor that is higher rated than you may normally use.
If you're unsure, get a colleague to have a look before you start.