The most common and most likely answer to this crossword clue is the 4 letter word PUMP
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More clues leading to the result PUMP
Buddy explains!

The straight part
We know that "Quiz to identify/type of shoe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quiz to identify/type of shoe = pump.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 PUMP mean?
PUMP noun- A device for moving or compressing a liquid or gas.
- An instance of the action of a pump; one stroke of a pump; any action similar to pumping
- A device for dispensing liquid or gas to be sold, particularly fuel.
- A swelling of the muscles caused by increased blood flow following high intensity weightlifting.
- A ride on a bicycle given to a passenger, usually on the handlebars or fender.
- The heart.
- (British slang) The vagina.
- To use a pump to move (liquid or gas).
- (often followed by up) To fill with air.
- To move rhythmically, as the motion of a pump.
- To shake (a person's hand) vigorously.
- To gain information from (a person) by persistent questioning.
- To use a pump to move liquid or gas.
- To be going very well.
- To kick, throw or hit the ball far and high.
- To pass gas; to fart.
- To pass (messages) into a program so that it can obey them.
- (British slang) To copulate.
- To weightlift.
- A type of shoe, a trainer or sneaker.
- A type of women's shoe which leaves the instep uncovered and has a relatively high heel, especially a stiletto (with a very high and thin heel)
- A dancing shoe.
- A type of shoe without a heel.