Girl rested in middle of week (6)
I believe the answer is:
elaine
'girl' is the definition.
'rested in middle of week' is the wordplay.
'rested' becomes 'lain' (lying is a kind of resting).
'in' indicates putting letters inside.
'middle of' says to take the centre.
The middle letters of 'week' are 'ee'.
'lain' inserted within 'ee' is 'ELAINE'.
(Other definitions for elaine that I've seen before include "Name" , ""The lily maid of Astolat"" , "Woman" , "-- Paige, singer" , "-- Paige, singer/actress" .)