Pause the log shipping jobs that restore. Let new logs continue to be run on the primary and copied over.

Bring the DR database online (with recovery) and test if things are OK.

Once you are done, do a restore of your full backup with norecovery and then start restoring logs. The jobs may or may not pick up at the right sequence, depending on when you made the backup, so you might need some manual restores of logs (with norecovery) to get to the point where the automated jobs pick up.