The most common and most likely answer to this crossword clue is the 4 letter word EDDA
I've seen this crossword clue in The Daily Telegraph
E
D
D
A
More clues leading to the result EDDA
- English theologian introducing a series of stories
- Inspired, Dante pens literary collection
- English theologian introducing a collection of old Norse poems
- Was summing up abridged old poetry collection
- Somewhat revered, dark collection of legends
- Editor ultimately rejected a poetry collection
- Put on short, retrospective poetry collection
- Collection of old poems mostly summed up
- Work companion right when leaving cheesy village
- Studied Dante’s collected verse works
Buddy explains!

The straight part
We know that "Viking" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case viking = edda.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.