The most common and most likely answer to this crossword clue is the 5 plus 4 letter word GLOSS OVER
I've seen this crossword clue in Financial Times
G
L
O
S
S
O
V
E
R
Buddy explains!
The straight part
We know that "Hardly mention/what an undercoat may need" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hardly mention/what an undercoat may need = gloss over.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.