According to the Shared cM Project, a woman with 1053 shared cM could be your:
- First cousin (553-1225)
- Half aunt/niece (500-1446)
- Great aunt/niece (251-2108)
I have left out some relationships, such as great-grandchild, which seem unlikely.
Data from the DNA Detectives predicts the same relationships, giving all a range of 575-1330 cM.
Data from both sources make it extremely unlikely that your match is a half-sibling.
Because you took AncestryDNA tests, here are some next steps:
When viewing the match at AncestryDNA, click on "Shared Matches". That will tell you who else matches both you and your original match. You may be able to use this to tell if she's related to your father's mother or father's father, etc. (Even though their DNA isn't on Ancestry, the DNA of people related to one but not the other of them presumably is. If not, ask a 2nd cousin on your father's side to take a test.)
You can download your DNA from Ancestry and upload it to GEDmatch. If your match does the same, you can get more information on your DNA match there, including how much your X-chromosomes match. You can read about how to interpret that information or ask us in a new question.