The most common and most likely answer to this crossword clue is the 10 letter word REPARATION
I've seen this crossword clue in The Daily Telegraph
R
E
P
A
R
A
T
I
O
N
Buddy explains!

The straight part
We know that "process of putting things right again" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case process of putting things right again = reparation.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 REPARATION mean?
REPARATION noun- (usually in the plural) A payment of time, effort or money to undo past transgression(s).
- The act of renewing, restoring, etc., or the state of being renewed or repaired.