To an extent, gaps in knowledge decline (4)
I believe the answer is:
sink
'decline' is the definition.
(sinking is a kind of declining)
'to an extent gaps in knowledge' is the wordplay.
'to an extent' indicates the answer is hidden within the clue (I've seen 'extent of' mean this (I've seen this in other clues)).
'SINK' can be found hidden inside 'gaps in knowledge'.
(Other definitions for sink that I've seen before include "Submerge; basin" , "Decline - in the kitchen" , "Subside" , "place of corruption" , "Go down (in the kitchen?)" .)