Can I safely use gypsum under a Spruce tree to help break up the existing soil (hard packed clay now) before tilling in compost and new topsoil?
I wouldn’t advise the use of gypsum — and especially not tilling –beneath a mature tree. Tree root systems lie in a narrow band fairly close to the soil surface. Tilling will damage the roots and, therefore, damage the tree. Also, raising the soil level significantly under the tree, with new topsoil for instance, will restrict respiration in the tree roots, which would effectively smother them.
However, I would encourage you to make annual additions of compost. The depth should be no more than two inches each year, and shallower near the trunk, never touching the bark. The compost will gradually help improve soil structure, and encourage beneficial soil microorganisms as well as earthworms, which are the earth’s own tillers.
Gypsum has been used in agriculture, but, its benefits for the horticultural gardener are in question.