The most common and most likely answer to this crossword clue is the 6 letter word MERCIA
I've seen this crossword clue in The Guardian
M
E
R
C
I
A
More clues leading to the result MERCIA
- Thanks to Nancy, amateur discovers old kingdom
- Clemency in short supply before overthrow of excellent old kingdom
- Norman thanks a part of old England
- Foreigners express gratitude with a chunk of Olde England
- Old kingdom beginning to adapt, with thanks to the French
- Angles seen here in mosaic remain reflex
Buddy explains!

The straight part
We know that "old kingdom" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old kingdom = mercia.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.