I have an Indian passport and currently am in UK on a Tier 2 ICT long term staff partner visa valid up to January, 2020. My question is whether I need an additional visa to visit Dublin, Ireland to meet my sister who is on a student visa in Dublin.
Yes, you will need a visa for the Republic of Ireland. The visa type is 'C' and when you apply, choose Visit (Family/Friend) visa.
You may have heard that some people with Indian passports can visit Ireland with certain UK visas, and vice versa, but it only applies if you have a short stay visa like a tourist visa, not if you have a long-stay visa.
Details here from the Irish Nationalisation and Immigration Service.