The oldest R1a-Z93 ancient sample in the Balkans was found in Bulgaria and is dated around 1675 BC. It ID is I2163 and you can read about it here.
https://www.nature.com/articles/nature25778#Sec16 But it lef no descendants since it is Z93*.
There is also the SZ1 sample from Szolad which was first reported as dating from 1000 BC but is now presented by MTA as an Avar sample from 700 AD.
To have an idea about how your line arrived in Greece, you would need to identify your specific subclade first. R-Y934 has several subclades with different distributions and a TMRCA of 4100 ybp, which authorizes various theories.
Regarding modern samples, all I could found is a R1a-Z93 member of the Greek DNA Project on FTDNA (it represents one on 24 other R1a lines). Since he is not specified further downstream, you can look (it is public) and compare the STR values to see whether he is close to you or not.