What does the Pasuk mean?
Rashi (citing Toras Kohanim): It means that a Kohen may not render himself Tamei for a wife who defiled him from his Kehunah whilst she was alive, 1 provided there is someone to bury her (she is not a Mes Mitzvah).
Rashbam: It means that a Kohen is not permitted to render himself Tamei for his deceased wife, because it desecrates his Kehunah. 4
Targum Yonasan #2: It implies that a Kohen may render himself Tamei for relatives only if they have not left the fold.
Hadar Zekenim: Even a master among his nation, i.e. the Kohen Gadol, a Kohen may not become Tamei for him; Da'as Zekenim - it is permitted only if he is his father, brother or son.
Moshav Zekenim (citing Toras Kohanim 5 ): When the Mes is among the nation (not a Mes Mitzvah), he may not be Metamei for it.
As we will learn in Pasuk 7.
Seforno: It is therefore befitting that he should behave in an aristocratic fashion so that he commands the respect of the people, confining his dealings with Mesim to members of his family, since their Kavod is his Kavod too (See Seforno). Ramban: It denotes importance, as in Shmuel 2, 6:2, Yeshayah, 16:8 and Shemos, 22:13.
Even when he is not serving in the Beis-ha'Mikdash.
I.e. the simple meaning of the verse applies to any wife. Rashbam points out that Chachamim expounded that the Isur is only for a Pasul wife. (PF)
Our text of Toras Kohanim expounds this on verse 1! It seems that Moshav Zekenim's text expounded it on this verse.