Puts away magazine admitting review is endless (8)
I believe the answer is:
deposits
'puts away magazine' is the definition.
'deposits' can be an answer for 'puts' (depositing is a kind of putting). I am not certain of the 'away magazine' bit.
'admitting review is endless' is the wordplay.
'admitting' indicates putting letters inside.
'review' indicates an anagram.
'endless' becomes 'depots' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'is' anagrammed gives 'si'.
'si' inserted into 'depots' is 'DEPOSITS'.
Can you help me to learn more?
(Other definitions for deposits that I've seen before include "Matter laid down or money in the bank" , "Despots I find making bank lodgements" , "Lays down-inbank account?" , "Lodges in bank" , "Lodgements or down payments" .)