Looks like daub, finding more to buy to fill gaps isn’t so easy anymore. But a hemp lime putty will go in thick and strong to fulfill the same role.
Or make your own with clay, mud, straw.
I’d get the gypsum off, should be relatively detached. Give it a gentle tap to delaminate/crack. A bit of steam helps too if needed. Then go over with new lime. Whether you retain the existing depends on its condition and key, and how well you can make a join between new and old. Old needs to be solid and then cut with a 45deg angle so the new plaster goes behind the old at the intersection. Then limewash or distemper over the lot.
Yeah making your own cob / daub is good fun and very intuitive and easy. Something like 1 part clay, 2-3 parts sand and 0.5 parts chopped straw (or hemp or hay or wool or whatever). Then smear it in with hands / trowels (after the typical damping down of the substrate first). Everyday people have been doing that for thousands and thousands of years without special training or fussy recipes.