Out-of-the-way part played by father (5)
I believe the answer is:
pater
'father' is the definition.
(old-fashioned term for father)
'out-of-the-way part played' is the wordplay.
'out of' means one lot of letters goes inside another.
'the way' becomes 'e' (Compass direction - East).
'played' indicates an anagram.
'part' with letters rearranged gives 'patr'.
'e' inserted inside 'patr' is 'PATER'.
'by' acts as a link.
(Other definitions for pater that I've seen before include "Taper away like father" , "Walter --, English essayist; father" , "A posh father, from Latin" , "Dad (Latin)" , "Old man" .)