I'm flipping irritated after one male entered the country (10)

'entered the country' is the definition.
(as in immigrating into another country)

'i'm flipping irritated after one male' is the wordplay.
'flipping' says the letters should be written in reverse.
'irritated' becomes 'grated' (grating is a kind of irritating).
'after' is a charade indicator (letters next to each other).
'one' becomes 'i' (Roman numeral).
'male' becomes 'm' (common abbreviation).
'im' back-to-front is 'mi'.
'mi'+'grated'='migrated'
'i'+'m'='im'
'migrated' put after 'im' is 'IMMIGRATED'.