Gambit / Taylor Kitsch should have appeared in a direct sequel for X3 - X-Men 4. But of course, for some reason Fox and company thought it was better to move forward with solo Wolverine films and a prequel X-Men film.
Also, it's just not Gambit. Others like Angel, Psylocke, Jubilee, Bishop, etc could have joined the team full time if we got X-Men 4, 5 and 6, as those films would have introduced newer characters or retconned previous versions for the team.
To this day I still find it a big blunder how X-Men Days of Future Past was followed by X-Men Apocalypse and X-Men Dark Phoenix, when they could have featured those mutants in the "present period" with the Wolverine, adult Jean, adult Storm, adult Cyclops, much older Beast, Colossus, Shadowcat, Iceman, Rogue, Colossus, much older Professor along with new faces. Instead we got these "younger version" sharing screentime with younger version of Magneto and Mystique...