The most common and most likely answer to this crossword clue is the 5 letter word DAIRY
I've seen this crossword clue in The Daily Telegraph
D
A
I
R
Y
Buddy explains!

The straight part
We know that "supplier of milk" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case supplier of milk = dairy.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 DAIRY mean?
DAIRY noun- (also dairy products or dairy produce) Products produced from milk.
- A place, often on a farm, where milk is processed and turned into products such as butter and cheese.
- A dairy farm.
- A shop selling dairy products.
- A corner store, superette or minimart.
- (chiefly in the plural) A woman's breast.
- Referring to products produced from milk.
- Referring to the milk production and processing industries.
- On food labelling, containing fats only from dairy sources (e.g. dairy ice cream).