The most common and most likely answer to this crossword clue is the 5 plus 3 plus 7 letter word UNDER THE WEATHER
I've seen this crossword clue in The Guardian
U
N
D
E
R
T
H
E
W
E
A
T
H
E
R
More clues leading to the result UNDER THE WEATHER
- Two separate articles in lingerie the worse for wear
- Sick of being rained on?
- Below par when Arthur teed off – gripping end to game
- Where some papers put the crossword gets you feeling sick
- Terribly rude, when theatre is off
- Subject to climatic conditions — suffering from cold?
- Indisposed subordinate, a British subject?
- Thunder cracking with energy – if caught, you’ll get ill
- Air passengers making descent may soon become so poorly
- Pull through, after he turned terribly sick
Buddy explains!

The straight part
We know that "Off-colour" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case off-colour = under the weather.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.