Drain part of eye, admitting problem (7)
I believe the answer is:
consume
'drain' is the definition.
(I know that drain is a more specific form of consume)
'part of eye admitting problem' is the wordplay.
'part of eye' becomes 'cone' ('cone' is part of 'eye').
'admitting' indicates putting letters inside (admit can mean to welcome in or accept).
'problem' becomes 'sum' (as in a mathematical problem).
'cone' enclosing 'sum' is 'CONSUME'.
(Other definitions for consume that I've seen before include "Use up" , "Eat, drink" , "Exhaust" , "Devour" .)