I got this message when installing SEAGATE disk recovery SW: "Premium Recovery Suite" can't be opened because Apple cannot check it for malicious software.

If there is a way to open it, Safely open apps on your Mac - Apple Support describes how.

If that software was bundled with a hard disk drive you're better off just deleting it. Most of those utilities are useless, at best.

I absolutely agree: you do not want to install or have any software/app included in an external drive. They do not need anything to be able to function. All you need to do is to make sure it is formatted for Mac (Mac OS Extended) with the GUID partition scheme; that is all. You simply use Disk Utility (Applications > Utilities) for that. While it is formatting, it will erase the drive.

I completely agree with @John Galt and @babowa. If you need to use this drive with Windows as well, then use Disk Utility to erase the drive as GUID partition and exFAT, otherwise follow @babowa's advice to prepare the drive for use only on the Mac.