Some Laws of Mourning for a Grandfather When the Father Already Passed Away

Do any laws of mourning apply to a person whose father passed away a few years ago, and now his paternal grandfather has passed away, and several of his uncles are sitting shiva for his grandfather?

He does not observe any mourning customs at all, since the custom to observe mourning is only out of respect for his father or mother who are sitting shiva. Since his father already passed away, there is no reason to observe this mourning.

It states in the Pitchei Teshuva, Yoreh Deah section 374, sub-section 4: ’See in Responsa Adnei Paz section 11, which discusses a case where a relative who would be disqualified from giving testimony together with him, and there are mourners here who are not yet aware of this, that, on the first Shabbos, there is no need to change his clothes from what he’s used to wearing, since the main reason for this custom is out of respect for the mourners. And this seems to be the opinion of the Remo who wrote that the mourning is observed out of respect for those who mourn with him. Therefore, here where there are no mourners it is obvious that he is exempt and even prohibited [from changing the way he dresses] because of the disrespect for Shabbos. But to me it seems that what the Remo wrote ’and what is customary’ applies even when there are no relatives who are mourning here; and so it is explained in the Darkei Moshe, where he states ’therefore one needs to change his clothes’.
And according to what we explained earlier, the source for the custom that is practiced today to mourn only together with his father and mother, and specifically when they are mourning for their father and mother. Therefore it is certainly out of respect for his father and mother, and not out of respect for the deceased. Therefore, when one’s parents are not alive, one does not observe even partial mourning.