Crossword Genius

Stored it here for a long time afterwards, with an old cloth over it (6)

Ross

I believe the answer is:

garage

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'stored it here for a long time afterwards' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.

'an old cloth over it' is the wordplay.
'an' becomes 'a'.
'old' becomes 'g' (I can't justify this - if you can you should believe this answer much more).
'cloth' becomes 'rag' (rag is a kind of cloth).
'over' means one lot of letters goes inside another.
'it' becomes 'e' ('e' can mean 'electronic' which is similar to 'IT').
'g'+'rag'='grag'
'a' inserted into 'grag' is 'garag'.
'garag'+'e'='GARAGE'

'with' is the link.

Can you help me to learn more?

(Other definitions for garage that I've seen before include "rock music" , "music genre" , "Music style; store (car)" , "Car's home (or hospital?)" , "Petrol seller; modern music style" .)

I've seen this clue in The Irish Times.
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