The most common and most likely answer to this crossword clue is the 9 letter word GODFATHER
I've seen this crossword clue in The Times
G
O
D
F
A
T
H
E
R
More clues leading to the result GODFATHER
- Good and moving death for mafia chief
- What Don might be to babe in arms, perhaps
- Gangster shot dead by chap who’s been collared?
- Daughter caught in a mist rising over the River Don
- Sponsor hated frog jumping around
- Sponsor daughter and gross husband to stop one after the other
- Follow retired fellow with dodgy heart, criminal mastermind
- Head of family more distant, speaking after recurrent trouble
- Mafia boss in rally about to execute rebellious fellow
- Originator of froth and aged rum
Buddy explains!

The straight part
We know that "Head of family" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case head of family = godfather.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 GODFATHER mean?
GODFATHER noun- A man present at the christening of a baby who promises to help raise the child in a Christian manner; a male godparent who sponsors the baptism of a child.
- A small post which is used in repairing a fence. For instance attached to and supporting an existing broken fence post.
- A mafia leader.
- To act as godfather or guardian to.