General Synonyms:
* Post-industrial
* Information-based
* Service-based
* Knowledge-based
* Technological
* Digital
* High-tech
* Advanced
* Modern
More Specific Synonyms:
* Post-manufacturing (emphasizes the shift away from industrial production)
* Post-Fordist (refers to the decline of mass production)
* Neoliberal (suggests the shift to a more market-driven economy)
* Globalization (focuses on the interconnectedness of the global economy)
* Information Age (highlights the importance of information and technology)
* Digital Economy (emphasizes the role of digital technology in the economy)
The best synonym for "postindustrial" will depend on the specific meaning you want to convey.