The most common and most likely answer to this crossword clue is the 3 plus 4 plus 7 letter word THE CATS PYJAMAS
I've seen this crossword clue in The Times
T
H
E
C
A
T
S
P
Y
J
A
M
A
S
More clues leading to the result THE CATS PYJAMAS
Buddy explains!
The straight part
We know that "simply the best" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case simply the best = the cats pyjamas.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.