Crossword Genius

Add padding to covers of Elgar by leading composer (9)

Ross

I believe the answer is:

upholster

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'add padding to covers of elgar by leading composer' is the definition.
I can't tell whether this definition defines the answer.

'add padding to covers of elgar by leading' is the wordplay.
'add padding' becomes 'holst' (I am not sure about this - if you are sure you should believe this answer much more).
'to covers of' means to remove the middle letters.
'by' says to put letters next to each other.
'leading' becomes 'up' (up can mean leading in a game).
'elgar' with its centre removed is 'er'.
'holst'+'er'='holster'
'holster' put after 'up' is 'UPHOLSTER'.

Can you help me to learn more?

(Other definitions for upholster that I've seen before include "cover chair" , "Cover furniture" , "Pack seats" , "Provide furniture with padding, springs etc" , "Provide furnishings" .)

I've seen this clue in The Times.
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