A girl with depth had to sell (7)
I believe the answer is:
carried
'a girl with depth had to sell' is the definition.
I can't judge whether this defines the answer.
'girl with depth had to sell' is the wordplay.
I cannot really see how this works, but
'girl' could be 'carrie' and 'carrie' is present in the answer.
'depth' could be 'd' (abbreviation in geometry) and 'd' is found within the answer.
No letters remain.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for carried that I've seen before include "Published" , "Bore" , "maintained" , "passed by majority" , "Transmitted; borne" .)