Fatherly relative of Terence leaving dead centre (3)
I believe the answer is:
dad
'fatherly relative' is the definition.
'dad' can be an answer for 'relative' (dad is a kind of relative). I'm unsure of the 'fatherly' bit.
'terence leaving dead centre' is the wordplay.
'leaving' indicates named letters should be taken away.
'dead'+'centre'='deadcentre'
'deadcentre' with 'terence' taken away is 'DAD'.
'of' is the link.
(Other definitions for dad that I've seen before include "Mum's mate" , "Papa" , "Old man" , "Pa" , "Pop, pater" .)