The most common and most likely answer to this crossword clue is the 4 letter word MULE
I've seen this crossword clue in The Guardian
M
U
L
E
More clues leading to the result MULE
- Cross — something afoot?
- Overheard to whimper like a baby, being cross?
- Obstinate fellow gets the slipper
- Drug smuggler gets cross
- Cross, the writer collars university student
- Stubborn person making a mess, wasting day after day
- Cross person who is …
- Smuggler‘s an obstinate individual … and slippery?
- Greek letter carried by the French animal
- Almost consider eliminating source of animal
Buddy explains!

The straight part
We know that "Obstinate fellow/slipper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obstinate fellow/slipper = mule.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 MULE mean?
MULE noun- The generally sterile male or female hybrid offspring of a male donkey and a female horse.
- The generally sterile hybrid offspring of any two species of animals.
- A hybrid plant.
- A stubborn person.
- A person paid to smuggle drugs.
- A coin or medal minted with obverse and reverse designs not normally seen on the same piece, either intentionally or in error.
- A MMORPG character, or NPC companion in a tabletop RPG, used mainly to store extra inventory for the owner's primary character.
- Any of a group of cocktails involving ginger ale or ginger beer, citrus juice, and various liquors.
- A kind of triangular sail for a yacht.
- A kind of cotton-spinning machine.
- To smuggle (illegal drugs).
- A shoe that has no fitting or strap around the heel, but which covers the foot.