The most common and most likely answer to this crossword clue is the 6 letter word PIAFFE
I've seen this crossword clue in The Times
P
I
A
F
F
E
More clues leading to the result PIAFFE
Buddy explains!

The straight part
We know that "one’s executed on the spot" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one’s executed on the spot = piaffe.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 PIAFFE mean?
PIAFFE noun- A calm, composed, elevated trot in place.
- To strut pretentiously, to parade about.
- To trot a horse with a high, slow, step, lifting the feet but without moving forward significantly.
- To ride a horse in this way.