How are your 3 switches connected right now? Are they connected to each oter or all of them are going to a Distribution switch?
If all of them are going to a distribution switch, you can connect the new one to direcly to the distri switch.
If your 3 switches are inter-connected, you just need to uplink this new swich to any of the existing ones and configure the trunk port, so you need only one link.
Cheers,
-amit singh