I have an external HDD, which is about 2 years old, that is producing a clicking noise. The drive is also not recognized in the disk management utility but appears in the connected storage as BUP Slim. So, is there any possibility of recovering the data ?
Clicking is usually indicative of a hardware error, often it's an issue with the heads resulting in an inability to read from the platters so the drive won't fully come online to present itself to the OS.
Software data recovery requires a drive that can be seen in disk management as well as a second drive to recover your files to.
Unfortunately, you need hardware level repair before data recovery can begin.
How important your data is up to you since it is usually quite expensive.
If you can live without your data then you have the option of opening the drive up and seeing what is wrong yourself but this me forgo being able to send it out for recovery later or it may increase the costs.
What happened to cause the issue may help. Was it dropped, dropped/knocked over while in use, other...?
Unfortunately, if the drive can't be read by software such as Recuva, then it becomes a more expensive situation. The bleakness of the replies is unfortunately the right tone to have.
What it comes down to is the best time to recover your data is before you lose your data. I hope you're able to recover your data, but even if you don't, I hope the lesson you take away is to have a proper backup solution in the future. Backing up important data on your PC is a basic part of PC ownership, no different than changing the oil in your car or the air filter in your furnace.