Antony,
I've had this happen on a couple of bags over the years.
If the "male" plastic clip has broken, you can usually buy a complete clip in a camping shop or on-line and get a cobbler to stitch in the replacement "male".
If the "female" (or both elements) has broken, I've cut away the plastic elements leaving two loops.
I've joined these together with a carabiner, one of the ones with a screw-gate fitting. It's sturdy yet you can take the strap off quite easily.
Before plastic clips, the joint was made with a "D" ring and a snap hook but these are not so readily available now.
Hope this helps
JT

Anthony
I had this problem on a new bag I bought, took it back to the seller and he exchanged it with a new one, I wouldn't try repairing it, I've always had good service from Titleist, either through the reseller or direct, I'm sure if you contacted them they'd offer you a solution.

The carbiners will do the trick as mentioned above. I've done it also.