The most common and most likely answer to this crossword clue is the 3 letter word GUV
I've seen this crossword clue in The Times
G
U
V
Buddy explains!

The straight part
We know that "Father" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case father = guv.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does GUV mean?
GUV noun- A form of address, usually to an unknown male or a superior. An informal form of sir.