Priest has little right to separate father and son (6)
I believe the answer is:
parson
'priest' is the definition.
'little right to separate father and son' is the wordplay.
'little' says to take the initial letters.
'to separate' is an insertion indicator.
'father' becomes 'pa' (pa can mean dad or father).
'and' is a charade indicator (letters next to each other).
The initial letter of 'right' is 'r'.
'pa'+'son'='pason'
'r' going into 'pason' is 'PARSON'.
'has' acts as a link.
(Other definitions for parson that I've seen before include "A rector or vicar" , "man of the church" , "Rector; clergyman" , "Anglican clergyman" , "Minister of religion" .)