An air of great wealth, for a start (4)
I believe the answer is:
tune
'an air' is the definition.
(air can mean a piece of music)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for tune that I've seen before include "Air, melody" , "Optimise the condition of" , "Improve quality" , "Of engine, adjust to run smoothly" , "'He who pays the piper calls the ...'" .)