The most common and most likely answer to this crossword clue is the 6 letter word FRIARY
I've seen this crossword clue in Financial Times
F
R
I
A
R
Y
More clues leading to the result FRIARY
Buddy explains!

The straight part
We know that "Religious house" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case religious house = friary.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 FRIARY mean?
FRIARY noun- House or dwelling where friars or members of certain religious communities live
- Like a friar; relating to friars or to a convent.