The most common and most likely answer to this crossword clue is the 4 letter word PONY
I've seen this crossword clue in The Guardian
P
O
N
Y
More clues leading to the result PONY
Buddy explains!

The straight part
We know that "Small glass/animal" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case small glass/animal = pony.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 PONY mean?
PONY noun- A small horse; specifically, any of several small breeds of horse under 14.2 hands at the withers.
- A small serving of an alcoholic beverage, especially beer.
- (New South Wales, Victoria) A serving of 140 millilitres of beer (formerly 5 fl oz); a quarter pint.
- Twenty-five pounds sterling.
- A translation used as a study aid; loosely, a crib, a cheat-sheet.
- A ponytail hairstyle.
- To lead (a horse) from another horse.
- To use a crib or cheat-sheet in translating.
- Crap; rubbish, nonsense.
- Of little worth.