I encountered it on Theogony of Hesiod on verse 44. I don't have any idea of my own. Anything is very appreciated.
Context: celebrate the august clan of the gods in song, Theogony of Hesiod, line 44
Clan has connotations of family or tribe. MW:
a group of people tracing descent from a common ancestor
August in this sense (with the stress on the second syllable!) means worthy of honour or respect. Again from MW:
marked by majestic dignity or grandeur
So august clan here means something similar to dignified family.
August can mean noble or majestic. So, without the sentence I would assume it means something like noble clan or venerable tribe or something like that.