Question
Will pruning a mature (25+ years) locust tree promote new growth?

Answer
If you are talking about the lower limbs re-sprouting leaves the pruning will not promote this. Pruning will promote new growth in the top branches. It sounds like the tree could use a cleaning pruning to take out the dead limbs. The best time to prune honeylocust is September and October but any time before leaf out is OK. I would recommend fertilizing the tree with a 13-13-13 fertilizer at the rate of 1 lb per inch of trunk diameter scattered around the tree and watered in good. And go ahead and prune the dead limbs and any other needing pruning Here is a web link to information on how to prune trees and also fertilizing.  http://www.treesaregood.com/treecare/pruning_mature.aspx
http://www.ext.nodak.edu/extpubs/plantsci/trees/h1035w.htm