The most common and most likely answer to this crossword clue is the 7 plus 8 letter word CLOSING CEREMONY
I've seen this crossword clue in Financial Times
C
L
O
S
I
N
G
C
E
R
E
M
O
N
Y
Buddy explains!
The straight part
We know that "the last part of the Olympics" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the last part of the olympics = closing ceremony.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.