The most common and most likely answer to this crossword clue is the 11 letter word NONETHELESS
I've seen this crossword clue in The Sunday Telegraph
N
O
N
E
T
H
E
L
E
S
S
More clues leading to the result NONETHELESS
Buddy explains!

The straight part
We know that "in spite of that" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in spite of that = nonetheless.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 NONETHELESS mean?
NONETHELESS adverb- Nevertheless.