The most common and most likely answer to this crossword clue is the 5 plus 6 letter word ROYAL ASSENT
I've seen this crossword clue in Independent
R
O
Y
A
L
A
S
S
E
N
T
Buddy explains!
The straight part
We know that "final approval" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case final approval = royal assent.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.