A jolly fuss about sick animal (9)
I believe the answer is:
armadillo
'animal' is the definition.
(armadillo is a kind of animal)
'a jolly fuss about sick' is the wordplay.
'a jolly' becomes 'arm' (I can't explain this - if you can you should give a lot more credence to this answer).
'fuss' becomes 'ado' ('ado' can be a synonym of 'fuss').
'about' means one lot of letters goes inside another.
'sick' becomes 'ill' ('ill' can be a synonym of 'sick').
'ado' enclosing 'ill' is 'adillo'.
'arm'+'adillo'='ARMADILLO'
Can you help me to learn more?
(Other definitions for armadillo that I've seen before include "S. Am. plated mammal" , "Mammal covered with horny plates" , "Dollar, ami for S American animal with bony plates" , "Toothless Native American" , "bony individual?" .)