Both exist and the ongoing one is worth the extra ten minutes, phones and one time copies drift apart within weeks. In order of ambition:

One time copy: export the contacts from Outlook as vCards, the Forward Contact, As a Business Card trick on a full selection followed by Save All Attachments in the draft gives you the vcf files. Combine them into one file with copy *.vcf combined.vcf in that folder if a single file suits better. Move the file to the phone and open it, Android's Contacts app offers to import a tapped vcf, or use the app's Import from storage option. Everything lands in whatever account the app asks you to choose.

Ongoing sync, the better answer: put the contacts into an account the phone syncs natively. Import the same vcf or an exported CSV into the Google account at contacts.google.com, or into an Outlook.com account, then confirm that account syncs contacts in the phone's settings. From then on edits made anywhere appear everywhere and the curated list stops forking.

The choice inside that: Google account if the phone is your center of gravity, Outlook.com if desktop Outlook is, since desktop Outlook connects to an Outlook.com account directly and your PST contacts can graduate into it wholesale, turning the local list into a synced one permanently.