I wish I had a clear sense of how this might develop but I don’t. It seems to me that there may be several areas of impact over the next few years:
+Diplomatic leverage of Museveni, Kenyatta, Kigame et al vis-a-vis the United States will be reduced as one of the main US “asks”–UN votes to maintain nuclear-related sanctions against Iran–drops away.
+While I do not foresee the current US administration raising expectations for other US priorities from these East African leaders, the next US administration might feel some greater freedom to address “the democratic recession,” declining press freedom, and other issues on the formal US policy list.
+Oil prices: if a lot more Iranian oil gets to market both in the near term from the immediate impact of lifting sanctions and the longer term from the increase in capacity associated with ramped up foreign investment, the prospects for oil production in Uganda and Kenya will be impacted, especially as related to the 2021-22 election cycle.
+Iran will reassume a stronger role in trade and finance in the region and thus compete more strongly with Israel, Saudi Arabia and the Gulf States.
+Iran will presumably increase its regional naval presence.
+The fall of the Gaddafi regime in Libya and subsequent sad state of affairs in that country reduced one major “petrocash” player in East African politics; an Iran less cash-strapped by UN sanctions might have aspirations to finance East African politicians aside from its espionage/security/terrorism enagement.