The clip on tie is not gentlemanly by any stretch of the imagination, but there are times when one has to be repaired. Although the clasps of most clip on ties are relatively simple, repairing them can be problematic as they're actually complex hinge joints. Reattaching the clasp can possibly damage the fabric of the tie, so you must tread lightly. Here are some ways to repair a clip on tie.
If your clip of the tie will not clasp shut, try using hot glue to set it in place. Make sure the clip is in the "closed" position and be mindful of the tie's fabric. Hot glue can damage the fabric and is quite difficult to remove.
Depending on the design of the clip, you may be able to use a safety pin to secure the clasp. Some clips are slotted to better hold the shirt fabric. It's possible to work a safety pin through this slot and pin the clip shut.
If the clasp hinge is buried too deeply in the fabric, or if it has come off completely, you can pin the tie directly to your shirt. Make sure the head of the safety pin is hidden either under the tie or under the shirt collar.
You can use a bobby pin (or two) to keep the tie pegged against your shirt collar. This may entail sliding the bobby pin into the same spot as the defunct clip or through the tie's knot.
You can also sew the clip shut with a needle and thread. Sew the clip as close to the hinge as possible, allowing as much length as possible to clip to your shirt collar.