The most common and most likely answer to this crossword clue is the 9 letter word BEESTINGS
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "First milk" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case first milk = beestings.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 BEESTINGS mean?
BEESTINGS noun- The first milk drawn from an animal (especially a cow) after it has given birth.
- A hypodermic puncture from a bee, resulting in envenomation and often involving the penetration and lodging of the stinger.
- (in the plural) Very small breasts.
- The first milk drawn from an animal (especially a cow) after it has given birth.