The most common and most likely answer to this crossword clue is the 4 plus 3 plus 4 letter word GIVE AND TAKE
I've seen this crossword clue in The Daily Telegraph
G
I
V
E
A
N
D
T
A
K
E
More clues leading to the result GIVE AND TAKE
Buddy explains!

The straight part
We know that "concession" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case concession = give and take.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 GIVE AND TAKE mean?
GIVE AND TAKE noun- The settling of differences through compromise and mutual concessions.
- A lively exchange of conversation.