The most common and most likely answer to this crossword clue is the 7 plus 5 letter word BEDTIME STORY
I've seen this crossword clue in Financial Times
B
E
D
T
I
M
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S
T
O
R
Y
More clues leading to the result BEDTIME STORY
- Base politician stifling newspaper account of late
- What to tell children of plot by politician
- Pillow talk possibly part of plot by Conservative
- Early Conservative cuddling daughter, perhaps 9
- Latest thing in child entertainment
- Relation to help youngster turn kipper?
- What might you tell children about to go out?
- It’s heard before getting off punishment, caught in plots with politician
Buddy explains!
The straight part
We know that "Pillow talk possibly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pillow talk possibly = bedtime story.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.