General:
* Air conditioner
* Air pollution
* Air pressure
* Air traffic
* Air travel
* Airplane
* Airport
* Assembly line
* Automatic teller machine (ATM)
Animals:
* Alligator
* Ant eater
* Antelope
* Armadillo
* Aardvark
Food and Drink:
* Apple pie
* Apple cider
* Apple sauce
* Asparagus
* Avocado toast
Other:
* Afternoon
* Aftershave
* Airplane
* Airport
* Armchair
* Artwork
* Armrest
* Arrowhead
* Aspirin
* Assistant
This is not an exhaustive list, as there are many compound nouns starting with "a".
Do you have a specific category in mind that you'd like to explore? Let me know and I can give you more examples!