Effect on GINI of eliminating poverty in China China eliminated extreme urban poverty this year and is on schedule to eliminate it in the rest of the country by the end of 2020. 

How do I calculate the approximate impact of this change for China's 2021 GINI?
Such calculation is extremely difficult, because all the factors involved in shaping the personal distribution of income: relative change in return to different skills/job (think e.g. on skill-biased technical change), demographical/educational composition change (e.g. many new educated young into the labour market), taxation/redustribution policies (if less poverty, less income support welfare needed?), variations in the functional distribution of income (ownership of financial assets?), etc. It also depends on whether you are measuring inequality at the individual or household level, and which equivalence scale you use in the latter. Not to mention that you need to somehow differentiate between urban and rural sectors to incorporate your change.

I can think of three options you can follow to get what you want:


Microsimulation: this requires to have a general equilibrium model where a population of (commonly) households are simulated, usually to analyse policy changes. For the case of China, an example is here. This is the best approach in terms of using economic theory, but it is very time-consuming.
Regression: here you estimate a regression to evaluate determinants of nation-wide inequality. Included in these determinants should be the rate of urban and rural poverty. Forecasting them (and other regressors) you can forecast future Gini. This method is a highly reduced-form approach and might be highly inaccurate or inconsistent (due to endogeneity, etc). Still, to get an idea, see this paper.
Percentile income growth: as suggested by ahorn, you could go atheoretical and simply predict income growth of each percentile. Then you can easily compute Gini. The plot of these percentile income growth are commonly known as "growth incidence curve". For an example on China see here (Figure 4).