The most common and most likely answer to this crossword clue is the 7 plus 6 plus 2 letter word GETTING AROUND TO
I've seen this crossword clue in The Times
G
E
T
T
I
N
G
A
R
O
U
N
D
T
O
Buddy explains!
The straight part
We know that "Making delayed start on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case making delayed start on = getting around to.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.