The most common and most likely answer to this crossword clue is the 8 plus 4 letter word STOPPAGE TIME
I've seen this crossword clue in The Daily Telegraph
S
T
O
P
P
A
G
E
T
I
M
E
More clues leading to the result STOPPAGE TIME
Buddy explains!
The straight part
We know that "final part of play" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case final part of play = stoppage time.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.