The most common and most likely answer to this crossword clue is the 6 letter word RESEAT
I've seen this crossword clue in Financial Times
R
E
S
E
A
T
Buddy explains!
The straight part
We know that "put in another chair" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put in another chair = reseat.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 RESEAT mean?
RESEAT verb- To provide (e.g. a room) with more, or new, seats.
- To seat (someone) again, to give somebody a different seat.
- To sit down again.
- To plug (something) back into its socket.
- To fit (something, especially a valve) back into its place.