Awfully vain yet showing innocence (7)
I believe the answer is:
naivety
'innocence' is the definition.
(I've seen this before)
'awfully vain yet' is the wordplay.
'awfully' is an anagram indicator.
'vain'+'yet'='vainyet'
'vainyet' with letters rearranged gives 'NAIVETY'.
'showing' acts as a link.
(Other definitions for naivety that I've seen before include "Ingenuousness" , "Lack of sophistication or worldliness" , "Quality of impractical innocence" , "Navy tie? (anag)" , "artlessness" .)