The most common and most likely answer to this crossword clue is the 9 letter word OVULATION
I've seen this crossword clue in The Guardian
O
V
U
L
A
T
I
O
N
Buddy explains!
The straight part
We know that "part of cycle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of cycle = ovulation.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 OVULATION mean?
OVULATION noun- The release of an ovum from an ovary.