The most common and most likely answer to this crossword clue is the 6 letter word FILING
I've seen this crossword clue in The Daily Telegraph
F
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L
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Buddy explains!

The straight part
We know that "office task" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case office task = filing.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 FILING mean?
FILING verb- To commit (official papers) to some office.
- To place in an archive in a logical place and order
- To store a file (aggregation of data) on a storage medium such as a disc or another computer.
- (with for) To submit a formal request to some office.
- To set in order; to arrange, or lay away.
- To move in a file.
- To smooth, grind, or cut with a file.
- To defile
- To corrupt
- Any particle that has been removed by a file or similar implement; a shaving.
- The act of storing documents in an archive; archiving.
- Something that has been officially filed; a document on file.