The most common and most likely answer to this crossword clue is the 10 letter word ACQUIESCED
I've seen this crossword clue in The Times
A
C
Q
U
I
E
S
C
E
D
More clues leading to the result ACQUIESCED
Buddy explains!

The straight part
We know that "Gave in" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case gave in = acquiesced.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 ACQUIESCED mean?
ACQUIESCED verb- (with in (or sometimes with, to)) To rest satisfied, or apparently satisfied, or to rest without opposition and discontent (usually implying previous opposition or discontent); to accept or consent by silence or by omitting to object.
- To concur upon conviction; as, to acquiesce in an opinion; to assent to; usually, to concur, not heartily but so far as to forbear opposition.