Brother of Carl's content, at the end of the day (5)
I believe the answer is:
friar
'brother' is the definition.
(I've seen this in another clue)
'carl's content at the end of the day' is the wordplay.
'content' indicates the central letters.
'at the end of' says to put letters next to each other.
'the day' becomes 'fri' (abbreviation for Friday).
The middle letters of 'carl' are 'ar'.
'ar' after 'fri' is 'FRIAR'.
'of' is the link.
(Other definitions for friar that I've seen before include "Male member of a mendicant religious order" , "Religious man" , "Father" , "Monk perhaps" , "Religious brother" .)