iReal Pro 7 and higher supports multitasking on newer iPad models. You can read PDF music charts while using iReal Pro.
More info about multitasking:
iOS slide over & split view: https://www.imore.com/how-use-slide-over-and-split-view-ipad-ios-11
Some users are using a PDF viewer app with either the chart from iReal Pro as PDF (you add text, lyrics etc. to the PDF) or PDFs of your existing charts (from Real books etc.) and if you need iReal Pro backing, this can be run in the background.
This method is discussed in the iReal Pro Forums: