How much does one have to stand up for a zakein? Does one only have to lift up from his chair partially or stand up completely?
In principle, the obligation is to stand up completely, as the Tur writes (Yoreh De’ah 244). See also Taz (244:4) and Bach.
Some, however, write that the obligation to stand up fully applies only to a talmid chacham, and not for somebody elderly, for whom a “hiddur” (making a motion of standing up slightly) suffices. See Me’iri, Kiddushin 32b, and see Shut Binyamin Ze’ev (Vol. 2, no. 243) and Aruch Hashulchan (244:10-12).
According to the simple ruling of the Shulchan Aruch, one must fully stand up for an elderly person and for a talmid chacham.
However, the Rambam and Shulchan Aruch (Yoreh De’ah 244:7) rule that a talmid chacham, even if he is young, does not need to fully stand up before somebody elderly, but makes a hiddur. The Levush (244:8) writes that the converse is also true (an elderly person for a talmid chacham): Because each of them has a virtue (age, or wisdom), a “hiddur” is sufficient.
Note that not every yeshiva student is considered a talmid chacham in this respect, as Teshuvos Vehanhagos (Vol. 3, no. 279) points out, and one should be particular to fulfill the full mitzvah of actually standing up. The Aruch Hashulchan (244:9) also stresses that even somebody elderly must make at least a “hiddur” for a talmid chacham, and possibly to stand up fully.
Some add that the elders of today forego their honor, and therefore a hiddur is generally sufficient, with the exception of one’s Rabbi, or a known “gadol.”
The Shach (244:11) already points out that the custom is to stand specifically for such known individuals, and see Shut Salmas Chaim (Rav Yosef Chaim Zonenfeld, Yoreh De’ah 326) who explains that although it is preferable to fulfill the mitzvah for all talmidei chachamim, the custom is based on the fact that there is a general mechilah on the part of elders and talmidei chachamim.