Minister's first job? To cut Iceland's taxes (7)
I believe the answer is:
imposts
'taxes' is the definition.
(impost is a kind of tax)
'minister's first job? to cut iceland's' is the wordplay.
'first' says to take the initial letters.
'job?' becomes 'post' (post is a kind of job).
'to cut' indicates putting letters inside.
'iceland' becomes 'is'.
The initial letter of 'ministers' is 'm'.
'm'+'post'='mpost'
'mpost' put into 'is' is 'IMPOSTS'.
(Other definitions for imposts that I've seen before include "customs duties" , "taxes" .)