There is a civil birth record for Ann Gleeson dated 12 December 1895. She was listed in Tulla Registration District. Her parents were: John Gleeson and Bridget Gleeson (formerly Tuohy),and they resided at Mount Allen.
This would appear to match the 1901 Census record that you referred to: http://www.census.nationalarchives.ie/pages/1901/Clare/Kyle/Mountallen/1086546/
There are Gleesons in the area, but I'm not sure if they would be related to this family. I can make enquiries if you like. You can email me directly at: email@example.com
It would appear that Ann was the youngest of this family.
I have also found a civil marriage record for John Gleeson and Bridget Tuohy who married on 15 June 1871 in Feakle. I'm attaching this as well.
As I stated above, if you would like more information, please let me know.