The most common and most likely answer to this crossword clue is the 11 letter word GOD-FEARING
I've seen this crossword clue in The Times
G
O
D
-
F
E
A
R
I
N
G
Buddy explains!
The straight part
We know that "Seriously religious" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case seriously religious = god-fearing.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 GOD-FEARING mean?
GOD-FEARING adjective- Following the precepts of a religious practice; respecting and revering God and His authority.