Keeper of everything, with increasing difficulty, keeping nothing (7)
I believe the answer is:
hoarder
'keeper' is the definition.
(someone who hoards or keeps hold of things)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for hoarder that I've seen before include "One saves" , "One with hidden store" , "Accumulator" , "Collector" , "Person unlikely to throw things away" .)