It depends entirely on the interface the drive is running, although I believe it is possible to get adapters.
In all likely hood it's running a possibly older generation of SATA, which would make it easy to put in to a more recent computer.
If the old drive had an OS on it, you won't be able to use that OS, you'll only be able to access certain files from it. If you don't need that however, it should be simple enough to format the new drive entirely and go from there.
Due to its age you might notice it being slightly slower than a modern drive, but not by too much.
(In both overall ability and interface speed limitations).
Another factor to consider is the size, if it's a 2.5" drive you may well need a caddy to secure it properly to the new case. If it's 3.5" most cases will come with more than one hard drive slot.
It should work fine, but do double check. If it's a super old drive running a non-modern interface you could probably pick up an enclosure for pretty cheap and just turn it into an external drive. Might be slightly slower but still usable.