The most common and most likely answer to this crossword clue is the 10 letter word RECOMMENCE
I've seen this crossword clue in Financial Times
R
E
C
O
M
M
E
N
C
E
Buddy explains!

The straight part
We know that "make new start" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make new start = recommence.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 RECOMMENCE mean?
RECOMMENCE verb- To begin again.