I have a 2021, M1 IMAC with two thunderbolt and two lightning connections in the back of computer. Can I get an adapter that will accept a male USB connector to connect my external hard drive back up?

Those are ThunderBolt 3 (USB-C) ports on the back of your M1 iMac.

What you need to plug in a USB external drive that has a USB-A plug, is a USB-C to USB-A adapter.

For the $20 Apple branded USB-C to USB-A adapter, see > USB-C to USB Adapter - Apple

For a $10 aftermarket Philips adapter that I know works with the M1 Mac's,

see > https://www.target.com/p/philips-usb-c-to-3-0-usb-a-female-adapter/-/A-79804275

and > https://www.amazon.com/Transfer-Charging-Connector-Portable-Convertor/dp/B0842CV8NY?

Yes, you can.

click here ➡️ Syntech USB C to USB Adapter Pack of 2 USB C Male to USB3 Female Adapter Compatible with MacBook Pro 2021 iMac iPad Mini 6/Pro MacBook Air 2022 and Other Type C or Thunderbolt 4/3 Devices Space Grey - Amazon.com

You can also buy a Dock that will expand what inputs are available to you. Navigate to macsales.com and click the Dock area, if you get yourself confused just call them. They are extremely helpful and can point you to the options that best suit your needs.