The most common and most likely answer to this crossword clue is the 7 letter word ROSSINI
I've seen this crossword clue in The Guardian
R
O
S
S
I
N
I
More clues leading to the result ROSSINI
- Composer and Antarctic explorer in one
- Somewhat cross, I niggle composer
- Composer admits small offence to French king
- Composer and Arctic explorer in one
- Chaplain is sorry for holding composer back
- Foreign ruler hosts small function for composer
- Antarctic explorer in India? Tell composer
- Tell the scorer
- Sins of old age were his: terrible sins hidden by king of France
- Composer with some dross in Italian
Buddy explains!

The straight part
We know that "Sins of old age were his" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case sins of old age were his = rossini.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.