It depends on what has happened on the principal after mirroring has been stopped. If you have a continuous log chain, then all you need to do is apply the transaction log backups to the mirror and restart mirroring.
If the log chain is broken, you have to reinitialize with a new backup and restore.
If the mirror is brought online, again - you have to start from the beginning again.
Jeffrey Williams
“We are all faced with a series of great opportunities brilliantly disguised as impossible situations.”
― Charles R. Swindoll
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Managing Transaction Logs