Welcome to the community, izier25!
Usually there shouldn't be any problem installing an old HDD in a different computer. Just make sure you have the data from the drive backed up elsewhere. Once you've installed the HDD on your laptop, you should be able to see the drive in Disk Management and re-format it from there. Check this tutorial from our KB that explains the whole process:
http/products.wdc.com/support/kb.ashx?id=mvXaJ1
Again, keep in mind that this would erase all the data on that drive, so make sure you have the data copied in another storage device.
Hope this helped. Keep me posted if you've got more questions!
SuperSoph_WD