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

The straight part
We know that "Tying up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tying up = bondage.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 BONDAGE mean?
BONDAGE noun- The state of being enslaved or the practice of slavery.
- (by extension) The state of lacking freedom; constraint.
- The practice of tying people up for sexual pleasure.
- Applied to clothing with many buckles, zips, etc., associated with punk and goth subcultures.