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Shut up nearest and dearest after losing second son (6)

Ross

I believe the answer is:

closet

I'm a little stuck... Click here to teach me more about this clue!

'losing second son' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'shut up nearest and dearest after' is the wordplay.
'shut up' becomes 'close' (I've seen this in another clue).
'nearest and dearest' becomes 't' (I can't justify this - if you can you should believe this answer much more).
'after' says to put letters next to each other.
'close'+'t'='CLOSET'

Can you help me to learn more?

(Other definitions for closet that I've seen before include "place to store gear" , "Study" , "Compartment for clothing in the US" , "North American cupboard" , "little room" .)

I've seen this clue in The Telegraph.
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