The most common and most likely answer to this crossword clue is the 8 plus 5 letter word COCKTAIL DRESS
I've seen this crossword clue in The Times
C
O
C
K
T
A
I
L
D
R
E
S
S
Buddy explains!
The straight part
We know that "Formal kit" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case formal kit = cocktail dress.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.