The most common and most likely answer to this crossword clue is the 7 letter word FROWNED
I've seen this crossword clue in The Daily Telegraph
F
R
O
W
N
E
D
Buddy explains!

The straight part
We know that "put on a serious face" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put on a serious face = frowned.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 FROWNED mean?
FROWNED verb- To have a frown on one's face.
- To manifest displeasure or disapprobation; to look with disfavour or threateningly.
- To repress or repel by expressing displeasure or disapproval; to rebuke with a look.
- To communicate by frowning.