Just put one of my ATs back on the bracelet it came with for the first time in months since I got it (it came overpolised so I just used straps) I noticed the clasp has a noticable gap and lots of play compared to my RM AT which is in like new condition and has zero play (same bracelet though) How do I go about correcting this? The stud that "clips in" looks perfect and unworn. Is this a spring issue?
Yes, likely the spring is not gripping that screw firmly enough, allowing the clasp to lift slightly.