European woman outside is Sweden’s first envoy (8)
I believe the answer is:
emissary
'envoy' is the definition.
(I know that envoy can be written as emissary)
'european woman outside is sweden's' is the wordplay.
'european' becomes 'E' (abbreviation e.g. EU).
'woman' becomes 'mary' (woman's name).
'outside' means one lot of letters goes inside another (some letters go outside others).
'sweden' becomes 's'.
'is'+'s'='iss'
'mary' placed around 'iss' is 'missary'.
'e'+'missary'='EMISSARY'
'first' is the link.
(Other definitions for emissary that I've seen before include "Person sent to negotiate" , "Someone sent on a mission" , "Government messenger" , "Delegate" , "I'm sent!" .)