Covering sweetheart with loving embrace (9)

I believe the answer is:

carpeting

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'covering' is the definition.
(carpeting is a kind of covering)

'sweetheart with loving embrace' is the wordplay.
'sweetheart' becomes 'pet' (both are terms of endearment).
'with loving' becomes 'caring' (similar in meaning. I am not sure about the 'with' bit.).
'embrace' means one lot of letters goes inside another.
'pet' going into 'caring' is 'CARPETING'.

Can you help me to learn more?

(Other definitions for carpeting that I've seen before include "clothing" , "may muffle footsteps" , "Being hauled over coals" .)

I've seen this clue in The Telegraph.

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