Woman, giddy aunt, carrying large spider (9)
I believe the answer is:
'spider' is the definition.
(tarantula is a kind of spider)
'woman giddy aunt carrying large' is the wordplay.
'woman' becomes 'tara' (**).
'giddy' is an anagram indicator.
'carrying' means one lot of letters goes inside another.
'large' becomes 'l'.
'aunt' with letters rearranged gives 'ntua'.
'ntua' going around 'l' is 'ntula'.
(Other definitions for tarantula that I've seen before include "web architect" , "A large hairy tropical spider" , "Creepy-crawly" , "hairy creature" , "A big hairy spider" .)