Extremely snobbish sanction having little depth (7)
I believe the answer is:
shallow
'having little depth' is the definition.
(I've seen this before)
'extremely snobbish sanction' is the wordplay.
'extremely' says to hollow out the word (remove centre letters) (letters on the extremes of the word are used).
'sanction' becomes 'allow' (I've seen this before).
'snobbish' with its centre taken out is 'sh'.
'sh'+'allow'='SHALLOW'
(Other definitions for shallow that I've seen before include "Without depth" , "Having little depth" , "12 [TWO DIMENSIONAL]" , "Not profound" , "Of waters, not deep" .)