Italian lady heading off –- extremely nescient, lacking in education (8)
I believe the answer is:
ignorant
'lacking in education' is the definition.
(I've seen this before)
'italian lady heading off extremely nescient' is the wordplay.
'italian lady' becomes 'signora' (I've seen this before).
'heading off' means to remove the first letter.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'nescient' with its middle removed is 'nt'.
'signora' with its first letter removed is 'ignora'.
'ignora'+'nt'='IGNORANT'
(Other definitions for ignorant that I've seen before include "Poorly-educated" , "Unaware, uninformed" , "Ill-educated" , "left in the dark" , "Devoid of knowledge" .)