The most common and most likely answer to this crossword clue is the 8 letter word ASSIGNED
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More clues leading to the result ASSIGNED
Buddy explains!

The straight part
We know that "Gave" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gave = assigned.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 ASSIGNED mean?
ASSIGNED verb- To designate or set apart something for some purpose.
- To appoint or select someone for some office.
- To allot or give something as a task.
- To attribute or sort something into categories.
- To transfer property, a legal right, etc., from one person to another.
- To give (a value) to a variable.