Inca dances, led by bird, that didn't go down well (7)
I believe the answer is:
titanic
'that didn't go down well' is the definition.
(reference to the Titanic's sinking)
'inca dances led by bird' is the wordplay.
'dances' indicates anagramming the letters.
'led by' says to put letters next to each other.
'bird' becomes 'tit' (tit is a kind of bird).
'inca' anagrammed gives 'anic'.
'anic' put after 'tit' is 'TITANIC'.
(Other definitions for titanic that I've seen before include "Twenty one [SHIP]" , "Of great size, like a sunken ship" , "Huge, like doomed liner that struck iceberg" , "Of enormous size, like the stricken liner" , "Nineteen twelve iceberg victim" .)