The most common and most likely answer to this crossword clue is the 6 letter word PAVING
I've seen this crossword clue in Financial Times
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More clues leading to the result PAVING
Buddy explains!

The straight part
We know that "Putting a cover over" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case putting a cover over = paving.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 PAVING mean?
PAVING verb- To cover something with paving slabs.
- To cover with stone, concrete, blacktop or other solid covering, especially to aid travel.
- To pave the way for; to make easy and smooth.
- The hard durable surface placed directly atop the ground, as on a street or sidewalk.
- Interior pavement, as in a cathedral.
- Pertaining to the material used for pavement, or to the surface itself.