Can one perform teshuva and be forgiven in such a case?
The Chida - Rabbi Chaim Yosef David Azulai explains in his commentary to the Pesach Haggadah, called Simchas HaRegel that:
if one transgresses a commandment for which the punishment is karet
(being cut off), only repentance, Yom Kippur and suffering remove the
The Rambam in his Mishneh Torah, Laws of Teshuvah 1:4 writes similary:
If a person violates [sins punishable by] karet or execution by the court and repents, Teshuvah and Yom Kippur have a tentative effect and the sufferings which come upon him complete the atonement.
The Rambam cites Psalms 89:33, in which it is said that only suffering atones completely in this case:
then I will punish their transgression with the rod, and their iniquity with strokes.
The Rambam writes:
He will never achieve complete atonement until he endures suffering for concerning these
Suffering, in addition to sincere repentance, Yom Kippur, cleanses from this type of sin. So the answer to the question if one can perform teshuva and be forgiven in the case of kares, the answer is yes, but it includes a big "if". It needs teshuvah, Yom Kippur and sufferings in order to be cleansed thoroughly.
Another, maybe a bit kabbalistic idea is given by Rabbi Chaim Vital. In his sefer שער רוח הקודש - Shaarei Ruach HaKodesh - The Gates of the Holy Spirit - explains that if one stays up all night long and learning Torah non-stop, each night will exempt one kares - each time. See this interesting article.
See also the work סוד ושורש העבודה שער הכולל by Rav Alexander Ziskind of Grodno explaining that one should study the subject his sin was about.
My own idea is that why we must study Torah in order to cleanse and get atonement for kareis, is because of the principle that "if one engages in Torah, suffering stays away from him" - Brachos 5a
Fasting is also listed as one of the possibilities as a tikkun - a rectification for kares. Refer to chapter 1 of Igeres HaTeshuva, Tanya, by the Alter Rebbe. The Kaf HaChayim on Orach Chayim 119:15 also mentions that tzedakkah - giving charity - can replace fasting.
The Rambam in The Laws of The Sanhedrin and the Penalties within their Jurisdiction writes:
Whenever a person sins and is lashed, he returns to his original state
My own interpretation, if I may, is that through suffering, we receive "lashes" and thus, in combination with teshuvah, we return to our original state, e.g. the state in which we haven't sinned.
This seems to be the language of the Mishnah in Makkos, saying:
Once he is flogged he is as your brother, as his sin has been atoned and he is no longer excised from the Jewish people; this is the statement of Rabbi Ḥananya ben Gamliel.
The idea that suffering is the same as "lashes" can be found in for example the commentary from Rav Ya’akov Ettlinger (Germany, 1798-1871), cited by Rav Aviad Tabory in the article "Renewal of Semikha (1538)"
He explains that:
The Rambam’s position is based on the Gemara on Yoma 86a which states that one who commits a sin that incurs karet achieves atonement only by performing teshuva and in addition experiencing yissurin (suffering).
Hagaon Harav Yitzchak Alfieh wrote that Taanis Dibbur, e.g. refraining from speaking for an extended amount of time, will serve as an rectification of kares.