The most common and most likely answer to this crossword clue is the 4 plus 4 letter word FULL STOP
I've seen this crossword clue in The Times
F
U
L
L
S
T
O
P
More clues leading to the result FULL STOP
- Period, when you’re ____ eating
- Period when stuffed shirt finally gets seduced by bribe?
- Dot‘s satisfied, getting back a lot of money
- Weed’s pulled up after busy period in 8
- End perfect stay
- Period when drunk’s drink’s withdrawn
- Fruity bar, nothing else
- Point, satisfied with small blouse?
- Complete rest period for Americans
- Period for Americans when this would be obvious advice to eater
Buddy explains!

The straight part
We know that "Period" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case period = full stop.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.