The most common and most likely answer to this crossword clue is the 7 plus 5 letter word MILKING STOOL
I've seen this crossword clue in The Times
M
I
L
K
I
N
G
S
T
O
O
L
Buddy explains!
The straight part
We know that "Item in parlour that drawer sits on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case item in parlour that drawer sits on = milking stool.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.