Fiction Professor taking week's rest (3,4)
I believe the answer is:
lie down
'rest' is the definition.
(to lie down is to have a short rest)
'fiction professor taking week's' is the wordplay.
'fiction' becomes 'lie' (I've seen this in another clue).
'professor' becomes 'don' (term for a university professor).
'taking' indicates putting letters inside.
'week' becomes 'w' (abbreviation).
'don' enclosing 'w' is 'down'.
'lie'+'down'='LIE-DOWN'
(Other definitions for lie down that I've seen before include "Rest (with or without sleep)" , "Short rest on bed/sofa" , "Take a rest (at length!)" , "Enid Low (anag.)" , "Relax" .)