Very busy introducing her elegant cat to its chambers (6)
I believe the answer is:
hectic
'very busy' is the definition.
(I've seen this before)
'introducing her elegant cat to its chambers' is the wordplay.
'introducing' says to take the initial letters.
The first letters of 'her elegant cat to its chambers' is 'HECTIC'.
(Other definitions for hectic that I've seen before include "Marked by intense agitation - fevered" , "'Rushed, madly busy (6)'" , "Frantic or feverish" , "Marked by intense activity" , "Frenetic" .)