Its game of thrones series and i need to know that the sentence is gramatically correct or not
I'm not sure exactly what point you are asking about.
"... that I have been waiting for" is fine, though some sticklers will tell you that you shouldn't end a sentence with a preposition - they are wrong, and you can ignore them.
"Ever" is not the right word, for several reasons. First, in its main use, it is only used in non-positive contexts (negative, or questions:)
Have you ever seen Game of Thrones?
I haven't ever seen Game of Thrones.
*I have ever seen Game of Thrones.
Secondly, its meaning in those examples is "at some time", not "for all time", or "for a long time", which is what you want. It is about occasions, or points in time, not spans of time.
What you want, I think, is
..that I have always been waiting for.
("Always" can be used for occasions or spans)
That is of course an exaggeration: it might be what you want, but I would say
... that I have been waiting for for so long.
(There is no problem with repeated "for": the first one is part of the phrasal verb "wait for", and the second is part of the temporal expression "for so long". In speech, the first "for" gets secondary stress, and is fully pronounced; the second "for" is spoken with a reduced vowel)