Composure of a Northern Ireland minister originally in actors’ union (10)

'composure' is the definition.
(I know that composure can be written as equanimity)

'a northern ireland minister originally in actors' union' is the wordplay.
'northern ireland' becomes 'NI' (abbreviation).
'originally' indicates taking the first letters.
'in' indicates putting letters inside.
'actors' union' becomes 'Equity' (Equity is the trade union for UK actors).
The initial letter of 'minister' is 'm'.
'a'+'ni'+'m'='anim'
'anim' going within 'equity' is 'EQUANIMITY'.

'of' is the link.