The most common and most likely answer to this crossword clue is the 10 letter word ECUMENICAL
I've seen this crossword clue in The Times
E
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More clues leading to the result ECUMENICAL
- Somehow, one uncle came to be advocating unity
- Cook dropping round coeliac menu to further Christian unity
- Universal anagram came in clue
- Non-sectarian English university situated in nice calm ground
- Catholic English copper with minion casing clubs
- European combined with Northern Ireland in backing thread promoting unity
- Set a clue about blokes in charge of the Christian church
- Universal Cinema production featured in cryptic clue
- Set a nice clue about Mass for Christian unity
Buddy explains!

The straight part
We know that "to further Christian unity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to further christian unity = ecumenical.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 ECUMENICAL mean?
ECUMENICAL adjective- Pertaining to the universal Church, representing the entire Christian world; interdenominational; sometimes by extension, interreligious.
- General, universal, worldwide.