The most common and most likely answer to this crossword clue is the 11 letter word WORSHIPPING
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More clues leading to the result WORSHIPPING
Buddy explains!

The straight part
We know that "attending religious services" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case attending religious services = worshipping.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 WORSHIPPING mean?
WORSHIPPING verb- To reverence (a deity, etc.) with supreme respect and veneration; to perform religious exercises in honour of.
- To honour with extravagant love and extreme submission, as a lover; to adore; to idolize.
- To participate in religious ceremonies.
- An act of worship.