You obviously have already one of the curves, it must stay as is and the new curve must have exactly opposite endpoint handles. Otherwise the new curve can be different, maybe based on other requirements which you want to keep secret.
One good thing to know: In Illustrator you can draw with the line tool a line segment which has the same direction and length as a handle. You can use such line as a jig to adjust the endpoint handle of a new curve.
Have snap to points and smart guides on. Activate the handles of an anchor by clicking the anchor with the direct selection tool. Draw the line by starting from the far end of the handle. The line start and end points snap and the line is not glued, you can use it later freely. An example:
In the top section the black lines are drawn along the handles.
In the middle section the handle visualization lines are moved to the assumed endpoints of the wanted new line. The original is moved aside temporarily to keep it in safe and the lines are locked to prevent gluing them to the red curve. The curve is drawn with the pen by simply dragging the pen along the handle lines.
Nothing prevents inserting more anchor points and even bringing the new curve from elsewhere. Convert the endpoints to corner points with the anchor type selection tool and then back to smooth ones by dragging the handles with the same tool. The tool snaps to the line end.
In the bottom section the original and the new curve are shown with handles.
Another good thing to remember: If you select a curve with the black arrow, hold the Ctrl key and drag one node of the curve, the whole curve follows and the dragged node snaps. Ctrl activates the white arrow temporarily.