The most common and most likely answer to this crossword clue is the 4 plus 5 letter word TAKE AFTER
I've seen this crossword clue in Financial Times
T
A
K
E
A
F
T
E
R
More clues leading to the result TAKE AFTER
Buddy explains!

The straight part
We know that "that you are a chip of the old block" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that you are a chip of the old block = take after.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.