The most common and most likely answer to this crossword clue is the 4 letter word HOUR
I've seen this crossword clue in The Daily Telegraph
H
O
U
R
More clues leading to the result HOUR
- Seductress denied one time
- Acclaim, losing no time
- Time to take heart from award
- Hold onto unworkable relationship, initially for some time
- Hope your other halves will meet this time
- King, say, not working for period
- Period house to the west of ancient city
- Endless suffering will stop over time
- Sort of figure that changes with time?
- It’s time I left alluring woman
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 = hour.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 HOUR mean?
HOUR noun- A time period of sixty minutes; one twenty-fourth of a day.
- A season, moment, or time.
- The time.
- (in the plural) Used after a two-digit hour and a two-digit minute to indicate time.
- (in the plural) The set times of prayer, the canonical hours, the offices or services prescribed for these, or a book containing them.
- A distance that can be traveled in one hour.