What does the cryptic crossword clue "Base display of arrogance greeting native American (7)" mean?

The definition is "Base". The wordplay uses a charade (building blocks). AIRS (synonym="AIRS") + HOW (synonym="HOW") = AIRSHOW The answer is AIRSHOW.

Base display of arrogance greeting native American (7)

Times Cryptic #28774 | 18 Down | 2023-11-30 flower