The most common and most likely answer to this crossword clue is the 5 plus 9 letter word SWORD SWALLOWER
I've seen this crossword clue in The Times
S
W
O
R
D
S
W
A
L
L
O
W
E
R
More clues leading to the result SWORD SWALLOWER
Buddy explains!

The straight part
We know that "circus act" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case circus act = sword swallower.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 SWORD SWALLOWER mean?
SWORD SWALLOWER noun- A performer who performs sword swallowing
- A person who performs oral sex on a man.