The most common and most likely answer to this crossword clue is the 6 plus 7 letter word SHROVE TUESDAY
I've seen this crossword clue in The Sunday Telegraph
S
H
R
O
V
E
T
U
E
S
D
A
Y
Buddy explains!
The straight part
We know that "time to get fat?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case time to get fat? = shrove tuesday.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.