While the wording of the proposed 36th Amendment to the Constitution does not explicitly require the Oireachtas to pass new law regulating abortion, this is likely to be necessary to protect the rights of pregnant people after repeal.
If the 8th Amendment is repealed, the Protection of Life During Pregnancy Act 2013 will remain in force; there will be no legal vacuum (see explanation here). However, that law is very restrictive as it only allows for abortion to be provided where a pregnant person’s life is in danger. This law was passed to give effect to the 8th Amendment of the Constitution. As the 8th Amendment only allowed for abortion where the life of the pregnant person was at risk, the law passed by the Oireachtas could not go beyond that.
If the 8th Amendment is repealed, then that will no longer be the case: the Oireachtas will be able to legislate for abortion in a wider range of cases.
Importantly, the 36th Amendment, on which people will vote on May 25th, says that “provision may be made” for the termination of pregnancy (our emphasis). It does not strictly require such a law (if it did, it would say that provision ‘shall’ be made for such a law).
Thus, on the face of it the Oireachtas will not be compelled to make a new law providing for the provision of abortion in a broader set of circumstances.
Although removal of the 8th Amendment will mean that the foetus no longer has constitutional rights (M v Minister for Justice and Others  IESC 14, para. 10.63), pregnant people will continue to have their full range of constitutional rights, including rights to life, to be free from torture, to privacy, and to bodily integrity. It is very likely that in order to vindicate and protect those rights (as the state is obliged to do), a new law will be required.
At the very least, it is likely that these constitutional rights will require the legalisation of abortion in cases of rape, incest, and ‘fatal foetal anomaly’. This would be in line with international human rights law. It can be argued that the Constitution also requires lawful abortion to be made available in situations of serious risk to health (to vindicate the right to bodily integrity and potentially the right to life). An argument can also be made that abortion ‘on request’ in early pregnancy is required to vindicate the right to privacy and to bodily integrity.
Thus, if repeal were not followed by a new law that allowed for abortion in a broader set of circumstances it is likely that a constitutional challenge to the restrictiveness of the Protection of Life During Pregnancy Act 2013 would succeed, at least to guarantee access to abortion in cases of rape, incest, risk to life, serious risk to health, and ‘fatal foetal anomaly’.
de Londras & Enright, Repealing the 8th: Reforming Irish Abortion Law (2018), Chapter 3 & Postscript