The MacBook Air (11-inch, Early 2015) has
- A Thunderbolt 2 port, with a Mini DisplayPort connector, that doubles as a Mini DisplayPort
- Two USB-A (USB 3.0) ports
MacBook Air (11-inch, Early 2015) - Technical Specifications - Apple Support
USB-A ports do not carry DisplayPort Alt Mode video, and plugging a USB-A to USB-C adapter into a USB-C port does not change that. If you are daisy-chaining a USB-A to USB-C adapter and a USB-C to HDMI adapter, this is why you are seeing no video signal.
I believe that what you need is
- A Mini DisplayPort (male) to HDMI (male) adapter cable, or
- A Mini DisplayPort (male) to HDMI (female) adapter, plus a HDMI to HDMI cable
https://www.amazon.com/s?k=mini+displayport+to+hdmi+adapter+cable
If you are trying to connect a 4K monitor, you may want to look for an adapter whose description says that it supports 4K resolution and a 60 Hz refresh rate. That might require an "active" adapter and a separate HDMI to HDMI cable.
https://www.amazon.com/s?k=mini+displayport+to+hdmi+adapter+active+60+Hz