To “tie up loose ends” is a familiar idiom, meaning “to deal with the minor consequences of a previous action; to tidy up, finish, or complete.”
"Tying up looses ends" will keep your past from hindering you presently. Loose ends can be distracting, and sometimes, paralyzing. Loose ends steal your mental concentration as they occupy your mind. You are unable to focus as you want to on more important things.
“Therefore gird up the loins of your mind” (1 Peter 1:13).
When Paul wrote these words, men didn’t wear pants; they wore tunics—skirts. To “gird your loins” meant to draw-up and tie your skirt into your belt so you could walk or run. This prevented the “loose ends” of the tunic from becoming snagged on something or entangled with your feet which would cause you to stumble or fall. No solider would consider going into battle without first ‘girding his loins.”
Spiritually, it means: don't let your loose thinking and undisciplined thoughts cause you to stumble into a wrong attitude. If you don’t tie up loose ends and tighten up your thinking, you will not be ready to respond to the need of the moment. Rather, you'll find yourself tied up in knots.