The most common and most likely answer to this crossword clue is the 7 letter word REBUILD
I've seen this crossword clue in The Daily Telegraph
R
E
B
U
I
L
D
More clues leading to the result REBUILD
Buddy explains!

The straight part
We know that "put back up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put back up = rebuild.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 REBUILD mean?
REBUILD noun- A process or result of rebuilding.
- To build again.