The most common and most likely answer to this crossword clue is the 5 plus 3 letter word TAWNY OWL
I've seen this crossword clue in The Daily Telegraph
T
A
W
N
Y
O
W
L
More clues leading to the result TAWNY OWL
Buddy explains!
The straight part
We know that "Somewhat rusty member of parliament?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case somewhat rusty member of parliament? = tawny owl.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.