Elizabeth, Thanks for the question

There can be multiple reasons for an older spruce to show branch death on top could be a result of desiccation, compromised roots, disease, insects, et al. Trimming off the top may help but the regrowth may not look aesthetically pleasing. If the tree is to be saved it would be important to determine the cause. Consultation with a certified arborist would be highly recommended (Find an Arborist (treesaregood.org)).

I hope this helps.