The most common and most likely answer to this crossword clue is the 4 plus 1 plus 6 letter word HAVE A LIE-IN
I've seen this crossword clue in Financial Times
H
A
V
E
A
L
I
E
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I
N
Buddy explains!
The straight part
We know that "Conduct group perjury session/stay in bed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conduct group perjury session/stay in bed = have a lie-in.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.