Since it's a MacBook, you probably use it as a "mobile" computer. You don't want to have it tied to an external drive all the time, even if the external drive is "portable." You can use the method described in this Apple document. It explains how to back up your complete iTunes library to an external drive. But the procedure is the same when putting your iTunes folder on an external drive, to use from there.
Manage and back up your iTunes media library - Apple Support
To summarize, "consolidate" your iTunes folder (which is in your user account Music folder) so it has all of your iTunes data. Then, copy that iTunes folder to the external drive. That is your "backup," but you can then use it as your ongoing iTunes folder. Launch iTunes as described in this document
Open a different iTunes Library file or create a new one - Apple Support
with the Choose Library option. Choose the iTunes Library.itl file in the iTunes folder you copied to external drive. Because that iTunes folder is initially the same, iTunes looks the same. But you can now expand your iTunes library further.
If you want to run iTunes while the external drive is NOT connected, and access the same music library, here's an extra option to consider. Sign up for iTunes Match, which is Apple's service that gives you an iCloud Music Library ($25 per year). Initiate the service with iTunes using your complete iTunes library on the external drive. iTunes Match matches or uploads your iTunes music library to iCloud, to create your iCloud Music Library.
On the MacBook, with external drive not connected, create a new iTunes library (see same link above). It opens blank (empty). However, when you sign in using your Apple ID, because you have an iCloud Music Library, you see your songs. You can stream your songs from iCloud, whenever and wherever the MacBook has a Wi-Fi connection to the Internet. No external drive needed.
When you are back home, connect the external drive and launch iTunes using the iTunes library on external drive. You are signed in with the same Apple ID, so you access the same iCloud Music Library, but your song files are all stored locally in this case. You should maintain this iTunes library so that you have a copy of all of your song files stored locally on that external drive.
When using MacBook in "mobile mode," all song files accessed from iCloud. When using MacBook in "stationary mode," all song files accessed from local storage. The iTunes Match services keeps things "in sync." And if you happen to have an iPhone (or other iOS device), you can access the same iCloud Music Library from it. This is Apple's info about iTunes Match
https://www.apple.com/itunes/itunes-match/