For general use:
* Hair covering: This is a more general term and could refer to other types of head coverings as well.
* Hair tie: This is less precise, but it could be used if you're talking about a hairnet in a casual setting.
For specific industries:
* Food service hairnet: This is a more specific term for hairnets used in food preparation.
* Industrial hairnet: This is a more specific term for hairnets used in manufacturing or other industrial settings.
Ultimately, the best way to find a substitute for "hairnet" is to consider the context in which you're using the word.