You are looking for an enclosure for the drive. Yes it is possible.
Laptop drives are 2.5". If it is older, it's interface may be IDE. Otherwise, it is a SATA drive. Your choices for an enclosure start by determining the drive's interface and then determining how you want to communicate with it. USB 2.0 is the cheapest, but is capped at roughly 25 MB/s. USB 3.0 enclosures can be had, and eSATA is the fastest. These will be fast enough to saturate most hard drives transfer rates.
If you don't need speed, get something like one of these for SATA drives or these for IDE drives.