Bumpity-bump

I've got several clumps of them growing and occasionally stems/trunks get broken by falling branches or fronds. Those stems never re-sprout except from the base. They're a clumping palm but are fairly slow growing. Eventually they will be tall. I've never tried cutting out stems to force new growth but it should work okay if the plant is healthy. When you say "they'd like it to look healthier", does it look sickly, or are they just concerned about it looking spindly? Because, spindly is what that species looks like, it's not a question of health.

I've never seen a pic of anyone's pruned, regrowing palm.

It's best to cut the growth back to the base of the plant.