The most common and most likely answer to this crossword clue is the 10 letter word VEGETATING
I've seen this crossword clue in The Times
V
E
G
E
T
A
T
I
N
G
More clues leading to the result VEGETATING
Buddy explains!

The straight part
We know that "Having a dull time" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having a dull time = vegetating.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.
What does VEGETATING mean?
VEGETATING verb- (of a plant) To grow or sprout.
- (of a wart etc) To spread abnormally.
- To live or spend a period of time in a dull, inactive, unchallenging way.