I have an old 11 inch macbook air from 2014

MacBook Air (11-inch, Early 2014) - Technical Specifications

That machine can drive a single external monitor, with a resolution of up to 2560x1440 pixels.

It has a Thunderbolt 1 port. This port has a Mini DisplayPort connector and can act as a Mini DisplayPort if you plug a Mini DisplayPort monitor or adapter into it.

The most natural connections would be

• Mini DisplayPort to Mini DisplayPort
• Mini DisplayPort to DisplayPort (only a connector size change; no signal change at all)
• Thunderbolt to Thunderbolt (for the specific case of an old 27" 2560x1440 Apple Thunderbolt Display)

You can also get Mini DisplayPort to HDMI adapters and adapter cables.

This Mac is too old to have USB-C (DisplayPort) output, so if you get a monitor that has a USB-C input (that she could use with some future computer), make sure it also has a DP, mDP, or HDMI input that she can use now.

Things to look for in a monitor:

• IPS panel
• 100% or near-100% coverage of sRGB. If no coverage is stated, assume the worst.
• Modern inputs of a type that she could use: DisplayPort, Mini DisplayPort, and/or HDMI. For HDMI, you will need an adapter or adapter cable.

Hello Joe Thomas3,

Thanks for reaching out to Apple Support Communities. We see you have some questions about a MacBook and using it to connect to an external hard drive, and we'd like to help. The following link may be able to help, as it walks through how to use an external monitor: Connect a display to your Mac - Apple Support

Regards.