The most common and most likely answer to this crossword clue is the 8 letter word COLONIAL
I've seen this crossword clue in The Daily Telegraph
C
O
L
O
N
I
A
L
More clues leading to the result COLONIAL
Buddy explains!

The straight part
We know that "of overseas dependency" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of overseas dependency = colonial.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 COLONIAL mean?
COLONIAL noun- A person from a country that is or was controlled by another.
- A house that is built in a style reminiscent of the period of the colonization of New England.
- Of or pertaining to a colony.
- Of or pertaining to a period when a country or territory was a colony.
- Of or relating to the original Thirteen Colonies of the USA.
- Of or relating to the style of architecture prevalent at about the time of the Revolution.