What is the application of the Newey-West estimator of variance in case that we have the presence of autocorrelation in our model?
Newey-West produces standard errors for coefficients estimated by OLS regression. The error structure is assumed to be possibly heteroskedastic and possibly autocorrelated up to some specified lag. Any autocorrelation at lags greater than that is ignored.
You run a linear regression, but suspect that the errors may have heteroscedasticity and/or autocorrelation in them. This can mess up your parameter covariance matrix, which means that your inference tests are all under question. For instance, t-statistics of parameter coefficients are quetsionable. Luckily, the coefficients themselves are probably fine. So, you want to adjust your parameter covariance matrix.
You could use heteroscedasticity and autocorrelation consistent (HAC) estimators to do it. Neweay West is one of these tools. You run it and get a new parameter covariance, which you can use for the inference, including parameter varainces and t-stats (p-values).