The most common and most likely answer to this crossword clue is the 11 letter word PROPINQUITY
I've seen this crossword clue in The Times
P
R
O
P
I
N
Q
U
I
T
Y
Buddy explains!

The straight part
We know that "Closeness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case closeness = propinquity.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 PROPINQUITY mean?
PROPINQUITY noun- Nearness or proximity.
- Affiliation or similarity.