The most common and most likely answer to this crossword clue is the 4 plus 4 plus 8 letter word MEET WITH APPROVAL
I've seen this crossword clue in The Guardian
M
E
E
T
W
I
T
H
A
P
P
R
O
V
A
L
Buddy explains!
The straight part
We know that "to gain acceptance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to gain acceptance = meet with approval.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.