Currently, none of the supported transformations for OSGB36 cover the Republic nor Northern Ireland. TM65_To_WGS_1984_2 is probably the best choice for conversion to WGS84 as the older transformations have no known accuracy values.
You can find out about supported transformations in ArcGIS in technical article 21327.
If the data's offshore, there's a transformation from OSGB36 to ED50 and you could then piece together other transformations. Accuracies are several meters.
You might check the online EPSG Geodetic Parameter Dataset to see if they have any other options. Note: I'm on the subcommittee that maintains the dataset.
UPDATE - December 11 2017
EPSG:6946, TM75 to ETRS89 (3) (Esri name: "TM75_To_ETRS_1989_3_NTv2"), and EPSG:6947, TM75 to WGS 84 (4) (Esri name: "TM75_To_WGS_1984_4_NTv2"), were added to ArcGIS Desktop version 10.3.1. That version was released in mid-2015.