How to predict when the pressure will change
Predictability of weather and climate is currently an active and lively research topic. I will try to giove some (very)  brief information on how it is normally done.

The best idea would be to use a weather (atmospheric) model, which is a numerical model that solves the Navier-Stokes Equations to bring prognostic information of the atmospheric state, for the next couple of days. This allows us to get a reasonably good prediction of high-low pressure zones within a week or so, which I intend is your goal.

Since you mentioned Windy.com, this is already a good source of information on weather prediction, probably one of the best compilation of weather models you can get nowadays. In the bottom right corner of the screan in windy.com (if using a desktop), you will see the acronyms GFS, ICON and ECMWF, for example. These are three models developed by possibly the three best centers in the world (from the USA, Germany and UK, respectively). A similar user-friendly interface, focusing on GFS is available at Earth Nullschool. They all bring a timer, so that you can choose the time of your prediction. Since you are asking specifically about a pressure system, I will assume you know how identify it in the images provided by these interfaces. 

The predictability of weather for the next few days is good, and the predictability of "seasonal climate" is not bad either. For some time scale in between (subseasonal), there has long been a "grey zone of predictability". This is where cutting-edge research in Climate Science currently takes place. Sources of predictability, generally comes from a thorough understading of climatic phenomena (e.g. ENSO, NAO) and their relationship with the predicted variable. The NAO is known to modulate weather in North America and Europe in the day-to-day time scale, for example. ENSO is the dominant factor for tropical latitudes, with a lower-frequency variability.

This type of research is normally done using numerical weather and climate models, not so different from the ones in windy.com, often combined with statistics. 

To reed further in the seasonal and decadal time scales.