As far as I am aware, links between the Provisional IRA (PIRA) and the Soviet Union were limited. The PIRA were mostly supplied by Irish Americans living abroad and famously by Gaddafi in Libya.
However the Official IRA (OIRA), which also operated in Northern Ireland during the troubles (although much smaller), was a largely socialist organisation and had extensive links with the USSR and other Communist states. The USSR and North Korea both supplied the OIRA at various stages during the troubles. In 1972, the KGB revealed their plan known as ‘SPLASH’, officially titled ‘Plan for the Operation of a Shipment of Weapons to the Irish Friends’. Additionally, members of the OIRA travelled to Russia and North Korea for training.
To understand why the USSR would prefer to work with the OIRA, despite being a much smaller organisation that was mostly involved in battles with the PIRA and other Republican groups, I’ll explain briefly the ‘plan’ that the OIRA had.
Essentially, they saw the troubles and sectarianism as an imperialist way for the ruling classes to keep the Proletariat separate. The OIRA planned to end the Troubles in any way, so that they could focus on uniting Catholics and Protestants as one Proletariat that would overthrow their imperialist overlord (Britain) and join the South in a 32 county socialist republic. The PIRA, by contrast, was focused on fighting a more traditional guerrilla war to liberate the North.