why wont my 2021 MacBook pro recognize my external hard drive, but worked on 2015 imac

With an M-series laptop, you need to authorize the connection. macOS will present a pop-up notice asking you whether it is safe to allow the external device to connect. Sometimes this pop-up may get hidden or not even appear. I find setting "Allow accessories to connect" in the Privacy & Security Settings to "Always when unlocked" is the best option (Apple has changed the wording, but "unlocked" is key option).

Allow USB and other accessories to connect to your Mac - Apple Support

Otherwise like @D.I. Johnson mentions, we need more specific details including the exact model of the Mac and version of macOS used (can be gotten by clicking the Apple menu and selecting "About This Mac"). And we need to know the exact model of the external drive and file system being used on it, and how that drive is being used....data only drive, backup drive (what backup software being used), etc.

How is the drive connected to the Mac? Have you tried connecting directly to the Mac and also tried using a powered USB3 hub (assuming a USB drive)?

Does the drive still work on the 2015 iMac?

BAnderson2574 wrote:

why wont my 2021 MacBook pro recognize my external hard drive, but worked on 2015 imac

Hard to say without more detail.

Please see: Writing an effective Apple Support Communities question - Apple Community

Have you set Finder to show external drives on the Desktop?

See the devices connected to your Mac - Apple Support

You can run Disk Utility First Aid on the drive and see if that can find and fix any issues.

Repair a storage device in Disk Utility on Mac - Apple Support

What brand and type (hdd/ssd) is this drive?

How old is it and what is the formatting?

What happens when you connect the drive?

Does the Mac show any sort of message when you connected the drive?