Your question makes no sense. An under cabinet mounted range hood is a wall mounted range hood. If you mean a free standing wall mounted range hood, then you need to do cabinet work, starting with removal of the cabinet that the current hood is attached to. Not ending with finishing the cabinet sides and redoing the crown. You will likely have drywall and electrical work as well.

outside vented? that makes a big difference. wall mount will not fit under a cabinet- the clearance will not work. your choices are few, unless you remove the upper cabinet. vent inserts offer low profile but used in custom work & usually cost more. function over form in the kitchen world.

post a pic of what you have and what you would like

Thanks everybody, it’s a remodel, existing vent is in the wall, had a microwave under cabinet for range hood, and yes want to replace with free standing range hood, no microwave but reinstall new cabinet and use existing vent in wall. Is this possible. Sorry the question made no since to you Sophie. Hope I explained it a little clearer this time . Freestanding, wall mounted I want that look whatever it’s called.