The most common and most likely answer to this crossword clue is the 10 letter word BIRTHRIGHT
I've seen this crossword clue in The Daily Telegraph
B
I
R
T
H
R
I
G
H
T
More clues leading to the result BIRTHRIGHT
Buddy explains!

The straight part
We know that "inheritance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case inheritance = birthright.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 BIRTHRIGHT mean?
BIRTHRIGHT noun- Something owed since birth, due to inheritance.