The most common and most likely answer to this crossword clue is the 8 letter word BASILICA
I've seen this crossword clue in The Daily Telegraph
B
A
S
I
L
I
C
A
More clues leading to the result BASILICA
- Church one left in no-frills area
- Fundamental article about the Italian church
- Herb, one Catholic overlooking a magnificent church
- Beginning to build a foundation for sandstone church
- Church the Italian put in primary area
- Saint in charge with a large church
- Church with barium compound used in glass
- Fellow in charge at Australian church
- It’s quartz, to a degree
- Herb I can mostly see in church
Buddy explains!

The straight part
We know that "papal church" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case papal church = basilica.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 BASILICA mean?
BASILICA noun- A Christian church building having a nave with a semicircular apse, side aisles, a narthex and a clerestory.
- A Roman Catholic church or cathedral with basilican status, a honorific status granted by the pope to recognize its historical, architectural, or sacramental importance.
- An apartment provided in the houses of persons of importance, where assemblies were held for dispensing justice; hence, any large hall used for this purpose.