Extremely touchy about old plaything (3)
I believe the answer is:
toy
'plaything' is the definition.
('toy' can be a synonym of 'plaything')
'extremely touchy about old' is the wordplay.
'extremely' says to hollow out the word (remove centre letters).
'about' means one lot of letters goes inside another.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'touchy' with its middle taken out is 'ty'.
'ty' enclosing 'o' is 'TOY'.
(Other definitions for toy that I've seen before include "Doll or teddy, say" , "Trifle with plaything?" , "Miniature (dog)" , "Small breed" , "Teddy or Dolly" .)