In most cases, if you make sure you set the sata mode on the new laptop to the same as the dead one (AHCI or IDE/Legacy mode), then it will more than likely work. (if they are both SATA).
However, newer hard drives are quicker, and you get a clean install of your OS which is always preferable. Better option would be get a USB HD caddy and just copy old files accross to the new machine.