Agency full of praise for a girl (7)
I believe the answer is:
claudia
'a girl' is the definition.
'agency full of praise' is the wordplay.
'agency' becomes 'cia' (CIA is an example).
'full of' is an insertion indicator.
'praise' becomes 'laud' (lauding is a kind of praising).
'cia' enclosing 'laud' is 'CLAUDIA'.
'for' is the link.
(Other definitions for claudia that I've seen before include "Female" , "- Schiffer, Ger. model" , "name for women" , "woman" , "Girl's name; CIA dual (anagram)" .)