Quietly admit to be lacking depth (7)
I believe the answer is:
shallow
'be lacking depth' is the definition.
(I've seen this before)
'quietly admit' is the wordplay.
'quietly' becomes 'sh'.
'admit' becomes 'allow' (allowing is a kind of admiting).
'sh'+'allow'='SHALLOW'
'to' acts as a link.
(Other definitions for shallow that I've seen before include "flimsy" , "12 [TWO DIMENSIONAL]" , "Not profound" , "Having little depth" , "justice" .)