The most common and most likely answer to this crossword clue is the 7 letter word MUMMIES
M
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More clues leading to the result MUMMIES
Buddy explains!

The straight part
We know that "Parents/those kept under wraps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case parents/those kept under wraps = mummies.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 MUMMIES mean?
MUMMIES noun- An embalmed human or animal corpse wrapped in linen bandages for burial, especially as practised by the ancient Egyptians and some Native American tribes.
- (by extension) A reanimated embalmed human corpse, as a typical character in horror films.
- (by extension) Any naturally preserved human or animal body.
- A brown pigment originally prepared from the ground-up remains of Egyptian animal or human mummies mixed with bitumen, etc.
- A pulp.
- A substance used in medicine, prepared from mummified flesh.
- A sort of wax used in grafting.
- To mummify.
- (usually childish) mother.