Hi Faye,
Unfortunately my search for anything related to Esther Clarke has not turned up much. Since she and Michael Keegan married in 1844, it's likely her baptism was before records began in Kinnegad. Assuming, of course, that she was born there.
I had focussed on attempting to find a civil death record for her (under Esther Keegan) in Mullingar, any time from 1864 to 1901 (she's not in the 1901 census that I could see). Unfortunately, the only record that may have matched was a "Hestor Keegan" 1813-1884. No other record seems to match in any registration district up to 1930.
If she was born in 1813, then she got married at 31 (1844) and had children until she was 51 (1864), so seems quite unlikely! Of course, her age at death could have been recorded incorrectly.
I might get that record to eliminate it from our investigations though.
One other piece of information is that Esther Clarke/Keegan's daughter, Esther (my ancestor), married in Dublin and her husband's witness was a Thomas Clarke. It could be a coincidence or this could be a cousin or relative of my Esther. Tracking back that line may shed more light on the Clarkes, potentially.
Alan.