Part 1. Transfer Playlist between Spotify Accounts
Although Spotify doesn't integrate the feature to import playlists, but it is not difficult to structure them manually. Besides, many free online playlist converters are available to help. They can export Spotify playlist to text file such as Excel, CSV, JSON so that you can import them to the new account later.
Use Spotify Desktop Client
This is the most intuitive way, you don't need any other tools just the Spotify app.
Step 1. Login your Spotify desktop program with the old account and password.
Step 2. Right-click on your playlists and choose "Collaborative Playlist" to make them editable for others.
Step 3. Drag & drop all the playlists to the desktop of your computer.
Step 4. Sign out of the old account and login with your new Spotify account and password.
Step 5. Drag & drop to import the playlists to left side bar one by one
Use Third-Party Spotify Playlist Copier Online
If you have hundreds or thousands of playlists, the above way will take you long time. To make it easier, you can try the online playlist converters such as playlist-converter, Soundiiz, PlaylistBuddy, Exportify, SpotMyBackup.
SpotMyBackup is a web app that let you export or import playlist to text within a few clicks. You can follow the steps to transfer playlists between Spotify accounts.
Step 1. Visit Spotmybackup website.
Step 2. Login with your old Spotify identification, it will load all the songs and playlists. If you have a large music library, it may take a long time.
Step 3. When all the data are loaded, you can one-click "Export" to export all playlists to a JSON text file.
Step 4. Log out the old account and sign in with your new Spotify account.
Step 5. Click "Import" and then choose the JSON file you have exported to import.