The most common and most likely answer to this crossword clue is the 6 plus 7 letter word MASTER BUILDER
I've seen this crossword clue in The Times
M
A
S
T
E
R
B
U
I
L
D
E
R
Buddy explains!
The straight part
We know that "Expert putting up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case expert putting up = master builder.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.