If a ribbed jumper cuff has opened where its two ends meet, the repair needs to close the seam and still let the cuff expand over the hand. First make sure the thread at the join failed and the ribbing itself has not torn or started to unravel.
Identify which seam has opened
Turn the sleeve inside out. A vertical opening down the cuff is its side join. A gap running across the sleeve where the cuff meets it is a different seam, often joining fabrics with different amounts of stretch. Follow the original thread and compare the other sleeve. For a simple vertical opening, align the ribs with the original edge and mark where the good stitching resumes on both ends.
Keep the cuff at its resting width
Match the original seam allowances, clip the two edges together and avoid stretching one more than the other. Test your stitch on similar knit. With a machine, follow its instructions for the appropriate needle and a stretch-capable stitch. A narrow zigzag may suit a stable knit; a bulky knit or tiny cuff may be easier to control by hand with a flexible stitch suited to its construction. Sew the original join, starting and finishing in sound stitching. Check the sleeve is not caught in the repair.
Test before trimming or finishing
Spread the cuff gently to the width it needs to reach when putting on the jumper. If it will not open comfortably, the stitches are too rigid or the seam is too far in. Check for loose knit loops along the inside edge. Where the ribbing has broken, stabilise the damaged loops before closing the seam. An open attachment seam involving several layers may be better assessed as a cuff replacement.
Check the feel on the wrist
Turn the sleeve right side out. The two edges should meet without a hard lump, and the ribbing should return to its usual width after the hand goes through. If it is still permanently stretched, sewing the side join alone will not restore its elasticity.