The most common and most likely answer to this crossword clue is the 4 letter word POPE
I've seen this crossword clue in The Times
P
O
P
E
More clues leading to the result POPE
- Poet who lives in a small community in Rome?
- Father, key church leader
- Poet’s Latin work picked up on those central to dupery
- Church leader requires work, in padre's case
- Page concealed by one poet or another
- Father, eastern church leader
- Faith leader shot close to synagogue
- Innocent, maybe: a thousand and eleven fled Pompeii
- Innocent may be found in cheapo peepshows
- Pontificating leader in writer?
Buddy explains!

The straight part
We know that "Church leader" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case church leader = pope.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 POPE mean?
POPE noun- An honorary title of the Roman Catholic bishop of Rome as father and head of his church, a sovereign of the Vatican city state.
- (Coptic Church) An honorary title of the Coptic bishop of Alexandria as father and head of his church.
- An honorary title of the Orthodox bishop of Alexandria as father and head of his autocephalous church.
- Any bishop of the early Christian church.
- The ruffe, a small Eurasian freshwater fish (Gymnocephalus cernua); others of its genus.
- (Cumberland) The Atlantic puffin (Fratercula arctica).
- The painted bunting (Passerina ciris).
- The red-cowled cardinal (Paroaria dominicana).
- To act as or like a pope.
- To convert to Roman Catholicism.
- (alcoholic beverages) Any mulled wine (traditionally including tokay) considered similar and superior to bishop.
- (Russian Orthodoxy) A Russian Orthodox priest; a parson.
- The whippoorwill (Caprimulgus vociferus).
- The nighthawk (Chordeiles minor).