UK and Irish immigration requirements are different. If you plan to arrive into, leave from or travel within the Republic of Ireland you may need a separate visa. You can check whether you need a visa for Ireland here.
There are no routine immigration checks at the land border between the Republic of Ireland and Northern Ireland. However, this does not mean that you can enter Northern Ireland without the appropriate UK immigration permission.
If you travel to Belfast via the Republic of Ireland, you must make sure that you meet the immigration requirements for both Ireland and the UK before you travel. Depending on your nationality and circumstances, this may mean obtaining an Irish visa to enter Ireland as well as a UK visa or Electronic Travel Authorisation (ETA) to enter the UK.
An Irish visa does not normally give you permission to enter the UK, and a UK visa does not necessarily give you permission to enter Ireland. There are limited exceptions, including for some travellers eligible under the British-Irish Visa Scheme.
Please check the official immigration requirements for both countries before booking travel via the Republic of Ireland.