There are a few different ways to approach this problem.
One possibility is to transform your daily price/return data into weekly open, high, low, close data. You may then calculate the Yhang-Zhang or other suitable OHLC variance estimator (e.g., Garman-Klass, etc) as per the canonical approaches.
This approach is enumerated in this the attached spreadsheet. In the spreadsheet, given only daily close data and dates, a weekly OHLC series was constructed. The YZ estimator was then taken over the entire data range.
Another possibility is to perform a moving time-series analysis, which may be more appropriate if one believes that the variance is non-stationary. I've had success incorporating YZ into autoregressive moving average (ARMA) models, such as generalized auto-regressive conditional heteroskedasticity (GARCH) models. In order to do so, one starts by calculating the YZ error over each interval.
Note: The weekly YZ estimator is not likely to result in a more efficient estimate than the daily close-to-close estimator. It will, however, provide an alternate measure of dispersion.