Unusually alert, at closing time, at Rose's place (6)

I believe the answer is:

tralee

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'rose's place' is the definition.
The definition suggests a singular noun which matches the answer.

'unusually alert at closing time' is the wordplay.
'unusually' indicates an anagram.
'at' is a charade indicator (letters next to each other).
'closing time' becomes 'e' (I can't explain this - if you can you should give a lot more credence to this answer).
'alert' with letters rearranged gives 'trale'.
'trale'+'e'='TRALEE'

'at' acts as a link.

Can you help me to learn more?

(Other definitions for tralee that I've seen before include "Kerry town of Roses" , "'The Rose of ------': song/film title featuring a town in County Kerry, Ireland" .)

I've seen this clue in the Evening Standard.

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