After British downfall, Scotsman becomes European (9)
I believe the answer is:
ukrainian
'european' is the definition.
(I've seen this before)
'after british downfall scotsman' is the wordplay.
'after' says to put letters next to each other.
'british' becomes 'uk' (Great Britain).
'downfall' becomes 'rain' (rain is a kind of downfall).
'scotsman' becomes 'ian' (common Scottish name).
'uk'+'rain' is 'ukrain'.
'ukrain'+'ian'='UKRAINIAN'
'becomes' is the link.
(Other definitions for ukrainian that I've seen before include "from Chernobyl" , "Slav" , "eg from Kiev" , "Little Russian" , "East European" .)