Importance of people to have time under doctor (6)
I believe the answer is:
moment
'importance' is the definition.
(I know that moment is a type of significance)
'people to have time under doctor' is the wordplay.
'people' becomes 'men' (men are people).
'to have' is a charade indicator (letters next to each other).
'time' becomes 't' (abbreviation).
'under' says to put letters next to each other.
'doctor' becomes 'mo' (medical officer).
'men' put next to 't' is 'ment'.
'ment' put after 'mo' is 'MOMENT'.
'of' acts as a link.
(Other definitions for moment that I've seen before include "Brief period of time" , "tick" , "Short time - importance" , "little while" , "An instant in time - important" .)