… claims every side's lacking depth (7)
I believe the answer is:
alleges
'claims' is the definition.
(I've seen this before)
'every side's lacking depth' is the wordplay.
'every' becomes 'al' (I can't explain this - if you can you should give a lot more credence to this answer).
'side's' becomes 'ledges'.
'lacking' indicates named letters should be taken away.
'depth' becomes 'd' (abbreviation in geometry).
'ledges' with 'd' removed is 'leges'.
'al'+'leges'='ALLEGES'
Can you help me to learn more?
(Other definitions for alleges that I've seen before include "States without proof" , "Declares to be the case without proof" , "Asserts without proof" , "Claims" , "Holds" .)