The most common and most likely answer to this crossword clue is the 7 letter word MANHOLE
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The straight part
We know that "that goes deep under cover" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that goes deep under cover = manhole.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 MANHOLE mean?
MANHOLE noun- A hole in the ground used to access the sewers or other underground vaults and installations.
- A hole providing access to the inside of a boiler, tank etc.
- A man's anus, in a sexual context.