You can always have MC experience some moment of adversity, a high stress situation or strong emotion (positive or negative) and then use this to illustrate that, just because it lessened in severity as far as can be seen, it isn’t gone. I think how you go about it mostly depends on how important you want it to be and which other aspects of the character you want to highlight. Do you have any particular reason to choose a stutter over something else or do you view it as incidental? Do you have any models for the character, fictional or not, to inform the presentation of the stutter or the overall characterisation? I must admit that I was actually thinking about this post long after I had read it, mostly this afternoon when I was working on something else and a related topic came up (I study and tutor History and I was going over the murder of Caligula in which one of the ascribed motives to one of the conspirators is Gaius making a mockery of Chaerea’s effeminacy, with one account describing his voice as the target of ridicule). I came up with a few figures who might be of interest to you after that: Demosthenes of Athens (a famous orator and politician concerning whom the origin of the cure of putting pebbles in your mouth is usually related), Claudius I, the fourth emperor of Rome (his story is interesting because his accession was extremely unlikely, he is characterised in a hostile manner by most of the sources concerning his reign due in large part to his disability, including a stutter, and, despite this, there is much evidence that he actually did a pretty good job), then I also came up some pretty famous ones, King George VI (the subject of The King’s Speech), Winston Churchill and Joe Biden, as some more modern examples. Good luck, let us know how it goes :)