Is it permissable for the Gaboim to ask a Cohen to leave the shul so they may call up a non Cohen for the first Aliya, during Leining, in order to accomodate congregants who would otherwise possibly not receive an Aliya,and may have an entitlement in terms of a yortzeit or possibly that a Levy is not present,or that there may be 2 or 3 non Cohanim who might be commemorating a Yortzeit.
It is permitted to request this from the Cohen, but not on a regular basis, and only in times of need, such as the presence of a chiyuv who would otherwise not receive an aliyah.
Maharam Schik (59) writes that it is permitted to ask a Cohen to forego the first aliah, upon which the Cohen can leave the shul, or forego the aliah (the gabbai should call up somebody else “with the consent [mechilah] of the Cohen”) — it is better that he should leave the shul for the aliyah. However, he writes (61) that one should not do this on a regular basis, but only in a special time of need, a ruling echoed in Daas Sofer (18). The Chazon Ish used to be particular in this matter, and would not permit requesting a Cohen to leave (hanhagos Chazon Ish, chap. 5).
Several authorities write that on Mondays and Thursdays it is permitted to ask the Cohen to leave where there are chiyuvim in the shul (see Toras Chaim 135:8; Iggros Moshe vol. 3, no. 20; Minchas Yitzchak, vol. 2, no. 41; see also Mishnah Berurah 18). Kaf Hachaim 135:14 writes that where there are many guests in the shul, it is permitted to call one up for the first aliyah, and there is no need for the Cohen to leave, because it is clear that he is not receiving the aliyah on account of the presence of many guests. I think this halachah would be hard to apply today, because the general custom is to always give the first aliyah to the Cohen.
Teshuvah Me’ahavah (91) stresses that the Cohen cannot be forced to forego his place, and a number of authorities therefore write that the first aliah should not be sold (see Aruch Hashulchan 135:23; Shivas Tzion (6); Beis She’arim (6); Avnei Tzedek (9); see also Mishnah Berurah 135:18 concerning calling up a non-Cohen where the custom is to do so).