A disinclination to move in time to cover it up (7)
I believe the answer is:
inertia
'a disinclination to move' is the definition.
(I've seen this before)
'in time to cover it up' is the wordplay.
'time' becomes 'era' (I've seen this before**).
'to cover' indicates putting letters inside.
'up' is a reversal indicator (in down clue: letters go upwards).
'it' written backwards gives 'ti'.
'era' going around 'ti' is 'ertia'.
'in'+'ertia'='INERTIA'
(Other definitions for inertia that I've seen before include "Lack of activity" , "Apathy" , "Stagnating state" , "'Sluggishness, indolence (7)'" , "Apathetic state" .)