Composted manure is a good source of phosphorus, potash, carbon, and sodium. It is a great substitute for rock phosphate and potassium sulfate, if your soil can stand the sodium that usually accompanying manures (we like to see sodium at 1% or less of total CEC). Compost is highly bio-active, and will provide a biological path for phosphorus assimilation when the ionic path is closed by high pH. Studies at Colorado State University show rock phosphate is ineffective at high pH, but that manure and manure based compost are effective. And (or), there is a high P fish fertilizer you may want to try if you have a high pH soil. Rock phosphate and bonemeal are especially unavailable to the plants if the pH is over 7.5. Instead, use composted manure, or mix rock phosphate or bonemeal or bone char into an active compost pile, then dig in the finished compost.
Unless your compost is tested for mineral levels (such a test costs in the $150 range), you won’t know how much to apply for P&K deficits. Make an educated guess, maybe spread a layer 1 inch thick, then re-test next year to see the compost’s contribution to P&K.