The most common and most likely answer to this crossword clue is the 4 letter word MARA
I've seen this crossword clue in The Times
M
A
R
A
More clues leading to the result MARA
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The straight part
We know that "rodent" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rodent = mara.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 MARA mean?
MARA noun- A nightmare; a spectre or wraith-like creature in Germanic and particularly Scandinavian folklore; a female demon who torments people in sleep by crouching on their chests or stomachs, or by causing terrifying visions.
- A type of god that prevents accomplishment or success.
- Any malicious or evil spirit.
- Any caviid rodent of genus Dolichotis, common in the Patagonian steppes of Argentina.