Your Michael Pollard is in the Ballingarry parish register. This is unsurprising; the bulk of Pollard registrations are in that parish: of the 26 Pollard families on GV in Tipperary, 23 are in Ballingarry.
The record has:
Michael Pollard, bapt. 22 Feb 1836, son of Mick Pollard and Catherine Prout; sponsors John Pollard and Mary Prout.
My own ancestor was Tom Pollard, bp. 11 May 1833, son of John Pollard and Bridget Carroll. He married Judy Hackett in 1855 and immediately joined a group of Judy's relatives in sailing to South Australia. In 1860 the family moved to South Melbourne.
The parish register only starts in 1814, so we can't be certain about the relationship between your Mick Pollard (the father) and my John Pollard. They may have been brothers, or cousins.
Email me at crowley1950@outlook.com and I will send you pdf copies of my notes, including a typescript copy of Pollard entries in the Ballingarry parish register.