Can you? As long as you have the proper connections, yes you can.
SHOULD you? Probably not... Moving an HDD from one system to another can cause some issues with software, mostly with Windows & it's "hardware verification" as part of it's activation / verification system. If may require you to re-verify your license key with Microsoft (if not immediately, within 30 days) as a result.
Older HDD's may become a performance bottleneck as well, since most HDD's typically run at 5400 RPM (or 7200 RPM if you have a "High Speed" drive). HOWEVER, wear on the HDD may cause it to run at a slower speed. There's also potential integrity issues with wear & tear (as there's higher risk of bad spots appearing as a HDD ages from active use). You should check your HDD's health through the SMART (Self-Monitoring, Analysis and Reporting Technology) data to help determine if it's safe for you to recycle your old HDD.
Older HDD's also tend to be considerably smaller for storage space, although most internal drives are generally maxing out around 2 TB's (although external drives will exceed this). If the drive is relatively new (within 2-5 years), it may be large enough for general use as the typically minimum recommendation is around 500 GB's.
HOWEVER, this is ultimately your choice... Personally, I would just save the headaches & go with a new storage drive.
I hope this sheds some light on the subject.