Essentially, to replace the tile you will need to remove all the surrounding grout from the joints that suround the tile and then lever the tile out.
This can be done by either widening the crack so that you can get a chisel behind it to lever the tile off or use a hammer and chisel to gently chip the tile away. If this is not possible, you can use a drill and hardened tip drill bit to drill the tile out (drilling many holes in it to essentially remove it) or drill enough holes to get some purchase on teh tile to lever it off.
The key thing here is to be very careful and take your time so that you do not damage any surrounding tiles or put holes in the wall behind (if it is plasterboard). This is quite a delicate operation, but if you take your time can be done relatively easily.
Apologies or the misunderstanding - if you are just after a method of repairing the crack so that it is watertight again then I guess superglue or some epoxy-based solution would do this to a satisfactory level, but if you are looking to make the repair “invisible” then this is going to be much harder to achieve without actually replacing the tile.
After quick Google search for repairing cracks in ceramic tiles there are a few methods listed by various people involving using paint, artists pastels etc…. and a YouTube video that describes quite a good process that may be worth a try: https://www.youtube.com/watch?v=9XQshc098Jw
Without having tried this I obviously cannot vouch for how successful it is but may be worth a go
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