Palm trees grow new fronds every year and the oldest fronds die. When they turn brown they are dead and ready to be trimmed. This is usually only necessary once or twice a year.
Locally, here in Baja Sur, we often hire experienced palm tree trimmers that climb up the trunk of the palm, tie a rope around their waist and lock in their harnesses. They reach up and cut down the dead fronds. It is dangerous work so make sure your gardener has experience. Prices usually are charged depending on how tall your tree is.
When you cut off a stalk, it never grows back but new ones have room to grow above the old ones.
“The dead fronds on Mexican palms pose dangers of several types. They are extremely dry and papery, putting the palm at risk of fire. They provide habitat for undesirable animals such as rodents or snakes. Lastly, the dense fronds build up over time and may become structurally unstable to the extent that when someone tries to prune them, they all fall at once, posing a suffocation hazard.” SF Gate