Is there any specific period employee needs to wait to resign after TCS has retained someone?

Nothing is mentioned like that, leave as soon as they give you revised hike

Nope nothing as far as I am aware of. Its recommended to wait 6 months atleast or 1 year so you can solidify your new salary and make it positive for the next organisation that you aren't a jumper. But these days nobody really cares.

I have seen several posts stating that it is of 1 year and you won't get any promotion or increment till that period

I guess the duration is for 6 months