The most common and most likely answer to this crossword clue is the 4 letter word WEEK
I've seen this crossword clue in The Times
W
E
E
K
More clues leading to the result WEEK
- Period without power, we hear
- The Speaker’s feeble for a few days
- Little kindergarten’s opening in seven days
- Little kid's first few days
- How mobile phone network ultimately gives period of time
- Sequence of days inadequate for hearing
- Little man gives time
- Duration of feeble broadcast
- Reportedly a period of time to want a lack of will power
- Reportedly low on power for some time
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 = week.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 WEEK mean?
WEEK noun- Any period of seven consecutive days.
- A period of seven days beginning with Sunday or Monday.
- A period of five days beginning with Monday.
- A subdivision of the month into longer periods of work days punctuated by shorter weekend periods of days for markets, rest, or religious observation such as a sabbath.
- Seven days after (sometimes before) a specified date.