Ireland's old monarch trending (4)

I believe the answer is:

erin

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'ireland's' is the definition.
(poetic name for Ireland)

'old monarch trending' is the wordplay.
'old monarch' becomes 'ER' (Elizabeth Regina, ie Queen Elizabeth).
'trending' becomes 'in' (I can't justify this - if you can you should believe this answer much more).
'er'+'in'='ERIN'

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(Other definitions for erin that I've seen before include "(Literary name for) Ireland" , "Poetically, Ireland" , "Literary term for Ireland" , "Let ... Remember (song)" , "'Come back to ...' (emigrant song)" .)

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