The most common and most likely answer to this crossword clue is the 4 plus 10 letter word RUMP PARLIAMENT
I've seen this crossword clue in Financial Times
R
U
M
P
P
A
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L
I
A
M
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T
Buddy explains!
The straight part
We know that "17th century house after purge" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case 17th century house after purge = rump parliament.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.