Often an external hard drive will making clicking sounds due a loose connection, faulty cable or a faulty power adapter.
Unplug all of the cables and then visually check the cable connections. While still unplugged from any power source or computer connection, plug the cables in and out of their sockets on the external hard drive enclosure to see if any of the connections feel loose. If you find a loose connection, it can often be fixed by using a small screwdriver to re-correct the shape of a male or female connector. Also check the cables for any damage. Low voltage cables coming out of power adapters are often damaged when people wrap the cable tightly around the adapter when packing for storage.
If the connections and cable all appear fine the next thing to check is the power adapter (if your external hard drive has one). If you or a friend has an identical external hard drive enclosure try the power adapter from that to see if it resolves the problem.
The next step if none of the above have fixed your problem is to take the physical hard drive out of the external enclosure and either connect directly internally to a computer or connect to a known good external hard drive enclosure. If the hard drive clicking noise is now gone, then the external enclosure and cables should be replaced. If the hard drive is still making a clicking noise, then the fault is with the hard drive itself and you will need to troubleshoot further.