Q. What if someone constantly comes late because he gives a shiur to many people in another location, is it correct for the sake of the Torah of many, to skip P’sukei D’zimra?
Thank you.

A. Igrois Moishe (O.H. 4: 91) permits a Torah teacher who will be late for class to skip P’sukei D’zimra if he is unable to attend a later minyan. He rules similarly in the case of an employee who has to be at work in time or for someone who works for himself if there is a significant loss. However it is obvious that if he can be on time for davening, he certainly should do so.
On a chronically ill patient or an elderly and debilitated, Mekor Chaim (52) permits to shorten or skip P’sukei D’zimra according to his needs.
Similarly Shevet Halevy (8: 168) permits skipping P’sukei D’zimra when it is necessary for the Torah learning of many, such as a shiur. Ishei Yisroel (8: 8) mentions a similar heter for one that teaches a Torah class in regards to davening without a minyan, although he encourages to make every effort and daven with a tzibur
Horav Shlomo Miller’s Shlit”a opinion is that even when Talmud Torah of many is at stake, effort should be placed to try as much as possible to be early and say all P’sukei D’zimra. One should at least avoid late consistency by starting davening on time, some of the time.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a