According to free index for 1921 census she was born Isle of Wight and I note from online trees that she was born 20/11/1914.
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If we put this advice with the info found by Mckha489 re a possible birth as a result of WW1 it does not really tie in. WW1 was declared on 28/7/1914.
Some NZ families who had emigrated to NZ and were wealthy enough/had a tradition of sending their children from NZ for further education etc in the UK. My father's oldest three siblings were sent to England: male Sandhurst, female Bart's hospital, male Sandhurst.
The Clare family from NZ could also have done this. So this means that they would have been in England before the outbreak of war and met someone while there.
You/we really need to look for the marriages/movements etc of the Clare/Seabrook family children.
I don't know very much about DNA but could it be a female Clare who had the baby?
The Index mentioned would have the adopted name presumably? Would there ever be a case where the DoB was wrongly recorded in an adoption case?
I see the DoB in OP is mentioned as c1915. Is there a way to get some clarity on this? If she was born on IoW before the war started then the idea of a male Clare being the father is not as strong but if the child was born during the war then this becomes a possibility.