The most common and most likely answer to this crossword clue is the 8 letter word ENSHROUD
I've seen this crossword clue in The Times
E
N
S
H
R
O
U
D
More clues leading to the result ENSHROUD
Buddy explains!

The straight part
We know that "Put cloth cover on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put cloth cover on = enshroud.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 ENSHROUD mean?
ENSHROUD verb- To cover with (or as if with) a shroud