The most common and most likely answer to this crossword clue is the 5 letter word EXPEL
I've seen this crossword clue in The Guardian
E
X
P
E
L
More clues leading to the result EXPEL
- Throw out a slippery customer, pocketing ten pence
- Put out something evasive about Times page
- Throw out old coat shortly
- Get rid of former PM, half-heartedly
- Throw out slippery customer pinching 10p
- Professional leaving right and left boot out
- Discharge erstwhile gym class learner
- Get rid of shifty person hogging Times page
- Old footballer chucking last boot out
- Succeed in cutting cocaine quietly in bar
Buddy explains!

The straight part
We know that "Kick out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kick out = expel.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 EXPEL mean?
EXPEL verb- To eject or erupt.
- To fire (a bullet, arrow etc.).
- To remove from membership.
- To deport.