The most common and most likely answer to this crossword clue is the 15 letter word ACKNOWLEDGEMENT
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More clues leading to the result ACKNOWLEDGEMENT
- Tight low-necked garment not having Queen's acceptance
- Recognition of intelligence soldiers displayed in operation
- Thanks Ken endlessly in a fix
- Admission of something done to obtain information on workers
- We’d neglect man, OK? Not OK — recognition called for!
- Erudition shown by chaps in deed and expression of thanks
- Work over long weekend primarily means wrong profession
- A college principal should be aware of student's keenness, take time to ring people to give admission
Buddy explains!

The straight part
We know that "give admission" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case give admission = acknowledgement.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 ACKNOWLEDGEMENT mean?
ACKNOWLEDGEMENT noun- The act of acknowledging
- The act of recognizing in a particular character or relationship; recognition of existence, authority, truth, or genuineness.
- A reward or other expression or token of gratitude.
- An expression of gratitude for a benefit or an obligation.
- A message from the addressee informing the originator that the originator's communication has been received and understood.
- A response (ACK) sent by a receiver to indicate successful receipt of a transmission (See Wikipedia article on transmission).
- A recognition as genuine or valid; an avowing or admission in legal form.
- The act of a person admitting a child as their own.
- A formal statement or document recognizing the fulfillment or execution of a legal requirement or procedure.