Tree harsh old American disposed of in a song (9)

I haven't cracked this one yet — but the brilliant team at Times for the Times have:

Now I know this, and how it’s spelt, because of Reverend John Galbraith Graham MBE, setter for many years of the Grauniad Crossword, who picked the name because it’s the monkey puzzle tree. Here, it’s RAUCOUS for harsh minus the O(ld) US, set inside A ARIA, a song.