INDIRECT FLIGHTS via Tenerife, Gran Canaria or Madrid
There are inter-island flights from Tenerife north airport (25-minute flight), Tenerife south airport (40-minute flight) and Gran Canaria (50-minute flight) to La Palma.
From Gran Canaria, there are less flights per day than from Tenerife and they are usually more expensive as it's further to La Palma but you don't have to change airports.
Flights between the Canary Islands are with Binter and Canary Fly.
You can also fly to La Palma indirectly from any of the other Canary Islands, changing in Tenerife or Gran Canaria.
Or Madrid can be used as a hub for many different countries and then onward to La Palma.
For indirect inter-island flights, stay airside so you don't have to pass through security a second time.