The most common and most likely answer to this crossword clue is the 6 letter word PRIEST
I've seen this crossword clue in Financial Times
P
R
I
E
S
T
More clues leading to the result PRIEST
- Pirates at sea without a prayer?
- Art thou being nosy, vicar?
- Troublemaker receives Religious Instruction – from me?
- Peers ultimately support minister
- Father Ted at first undermining peers
- Clergyman most sorry to lose key
- Is Snoopy cartoon’s central character a father?
- Holy man supporting Pope Romanus’s cardinals, that is
- Clergyman forces open bottom of casement
- Stripe modelled for a clergyman
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 = priest.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 PRIEST mean?
PRIEST noun- A religious clergyman (clergywoman, clergyperson) who is trained to perform services or sacrifices at a church or temple
- A blunt tool, used for quickly stunning and killing fish
- The highest office in the Aaronic priesthood
- To ordain as a priest.