Installing an operating system (OS) on a MacBook Pro M1 (16-inch) 2021 model is a straightforward process that can be done using Apple’s built-in tools. Here’s a step-by-step guide to help you through the installation:

1. **Prepare Installation Media**: Ensure you have a stable internet connection and a USB flash drive with at least 16 GB of storage capacity. Download the macOS installer from the Mac App Store or Apple’s website.

2. **Create Bootable Installer**: Use the downloaded macOS installer to create a bootable USB installer. Connect the USB flash drive to your Mac and open Disk Utility. Format the USB drive as GUID Partition Map and macOS Extended (Journaled) format. Then, open Terminal and use the “createinstallmedia” command to create the bootable installer:

3. **Connect External Drive (Optional)**: If you want to install the OS on an external drive, connect it to your MacBook Pro M1 using a compatible cable or adapter.

4. **Start Installation**: Restart your MacBook Pro and hold down the Option (Alt) key immediately after the startup chime to enter the Startup Manager. Select the USB installer disk from the list of available boot options and press Enter.

5. **Install macOS**: Once the macOS installer loads, follow the on-screen instructions to begin the installation process. Choose the external drive or internal SSD as the installation destination, agree to the terms and conditions, and wait for the installation to complete. Your MacBook Pro may restart multiple times during the installation process.

6. **Set Up macOS**: After the installation is complete, your MacBook Pro will restart and boot into the newly installed macOS. Follow the on-screen prompts to set up your user account, language, region, and other preferences.

7. **Install Updates (Optional)**: After setting up macOS, it’s a good idea to check for and install any available updates. Go to System Preferences > Software Update to download and install updates for macOS and other installed software.

8. **Transfer Data (Optional)**: If you’re upgrading from an existing Mac, you can use the Migration Assistant utility to transfer your files, applications, and settings from your old Mac to your new MacBook Pro M1.

By following these steps, you can easily install macOS on your MacBook Pro M1 (16-inch) 2021 model, whether it’s a fresh installation or an upgrade from an existing os.