The most common and most likely answer to this crossword clue is the 5 plus 4 letter word PITCH INTO
I've seen this crossword clue in The Guardian
P
I
T
C
H
I
N
T
O
Buddy explains!
The straight part
We know that "Make a start on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make a start on = pitch into.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.