One awarded a degree put heads together mid-week (8)
I believe the answer is:
conferee
'one awarded a degree' is the definition.
(person whom a degree is conferred upon)
'put heads together mid-week' is the wordplay.
'put heads together' becomes 'confer'.
'mid-week' becomes 'ee' (the middle letters of 'week').
'confer'+'ee'='CONFEREE'
(Other definitions for conferee that I've seen before include "Person at meeting" , "Beneficiary" .)