Girl “I just met” with Greek character making music in Mexico (8)
I believe the answer is:
mariachi
'music in mexico' is the definition.
(type of Mexican music)
'girl i just met with greek character' is the wordplay.
'girl i just met' becomes 'Maria' ('I just met a girl named Maria' - West Side Story).
'with' is a charade indicator (letters next to each other).
'greek character' becomes 'chi' (letter from the Greek alphabet).
'maria'+'chi'='MARIACHI'
'making' acts as a link.
(Other definitions for mariachi that I've seen before include "street musicians?" , "one who performs music" , "Mexican folk music style" , "Mexican players" , "Traditional Mexican folk music" .)