Complex sentence: Mansfield did not become involved in much political activity when she lived in London; for example, she did not actively support the suffragette movement in the UK (women in New Zealand had gained the right to vote in 1893).
Split into simpler sentences: Mansfield did not become involved in much political activity when she lived in London. For example, she did not actively support the suffragette movement in the UK (women in New Zealand had had gained the right to vote in 1893).