The most common and most likely answer to this crossword clue is the 11 letter word SOLEMNISING
I've seen this crossword clue in The Times
S
O
L
E
M
N
I
S
I
N
G
Buddy explains!
The straight part
We know that "Seriously performing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case seriously performing = solemnising.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 SOLEMNISING mean?
SOLEMNISING verb- To make solemn, or official, through ceremony or legal act.
- To make grave, serious, and reverential.