The most common and most likely answer to this crossword clue is the 13 letter word PARLIAMENTARY
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More clues leading to the result PARLIAMENTARY
Buddy explains!

The straight part
We know that "related to MPs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case related to mps = parliamentary.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 PARLIAMENTARY mean?
PARLIAMENTARY noun- A parliamentary train.
- Of, relating to, or enacted by a parliament
- Having the supreme executive and legislative power resting with a cabinet of ministers chosen from, and responsible to a parliament.
- Of a class of train which, by an act of parliament, ran both ways along a line, at least once each day, at the rate of one penny per mile.