Salim (may Allah have mercy on him) said: Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) used to reject making a stipulation in Hajj and would say: "Is not the Sunnah of the Messenger of Allah (peace and blessings be upon him) sufficient for you? If one of you is held back from Hajj, he should perform tawaf of the House and (the sa'i of) al-Safa and al-Marwah, then he leaves ihram from everything until he performs Hajj the following year, and he should offer a sacrificial animal, or fast if he does not find one." Yunus said: Rabi'ah said: We do not know of any stipulation that is permissible in one's ihram.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 10123
Salim narrates from Ibn Umar (may Allah be pleased with them both) that he used to reject stipulations in Hajj and would say: Is not the Sunnah of the Messenger of Allah (peace and blessings be upon him) sufficient for you?
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 10124
Abd al-Razzaq narrates it from Ma'mar (may Allah have mercy on him), and in it there is an addition: "If someone holds back one of you, then when he reaches it (the House) he should perform tawaf of it and (the sa'i) between al-Safa and al-Marwah, then shave his head or shorten his hair, and Hajj is due on him the following year."
(b) The author says: In my view, if Abu Abd al-Rahman Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) had received the hadith of Duba'ah bint al-Zubayr (may Allah be pleased with her), he would have adopted it and would not have rejected making a stipulation in Hajj, just as his father did not reject it. And success is from Allah.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 10125