The most common and most likely answer to this crossword clue is the 9 letter word BEFRIENDS
I've seen this crossword clue in The Times
B
E
F
R
I
E
N
D
S
Buddy explains!
The straight part
We know that "Gets cosy with" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gets cosy with = befriends.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 BEFRIENDS mean?
BEFRIENDS verb- To become a friend of, to make friends with.
- To act as a friend to, to assist.
- To favor.