Sedimentary rocks are pushed down at subduction zones and changed into metamorphic by heat and pressure. This is one way metamorphism happens.
At subduction zones like off the coast of South America the ocean sediments from the Pacific Plate are pushed under the South American plate. The sediments are then subjected to heat and pressure that turn them into Metamorphic rocks.
If the rocks are pushed further into the crust and near the mantle the rocks are melted and turned into igneous rocks.
A piece of coal ( a sedimentary rock) can be changed artificially into a diamond ( a metamorphic rock) by subjected the carbon in the coal to extreme heat and pressure without the presence of Oxygen.
This is what happens under the earth surface when sedimentary rocks are buried and subjected to extreme heat and pressure.