Remove the hem on the sleeves of the sport coat using a stitch remover.
Unfold the fabric to see how much you have to work with. Put the jacket on and determine where the new hem should be placed. The sleeves should rest at your wrist when you're standing normally.
Fold the fabric at the location of the new hem and add straight pins to keep it folded over.
Turn the jacket sleeves inside out and iron the fold as added reinforcement while you sew the new hem.
Add a straight stitch about 5/8 of an inch from the fold using a sewing machine. Choose a thread color that matches the jacket.
Cut away any remaining fabric below the stitch to complete the hem.