All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There is no harm in using connections if it does not result in canceling a right, imposing a wrong, or acting as a mediator for something unlawful. There is no harm in using connections so that the university overlooks the admissions deadline as long as the responsible parties at the university consent to it and allow exceptions on the requirements for anyone it wants.
It should be noted that it is encouraged in Islam to intercede on behalf of others to help them with their permissible needs. The Prophet, sallallaahu ‘alayhi wa sallam, urged Muslims to intercede on behalf of people to help them fulfil their permissible needs, saying: “If one fulfills the needs of his brother, Allaah will fulfill his need.” [Al-Bukhari and Muslim]
Moreover, whenever a beggar or a person in need came to the Prophet, sallallaahu ‘alayhi wa sallam, he would say: “Intercede and be rewarded, and Allaah fulfills what needs He wills on the tongue of His Prophet.” [Al-Bukhari]
Allaah Knows best.