All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
There is some ambiguity in the question; but if you mean that you wish to ask someone to carry out the preliminary procedures on your behalf before you take the driving test and pay him in return for this service, then there does not seem to be any harm in doing that.
However, if you mean that you pay this employee to give you precedence over other applicants who came before you and started standing in the queue before you, then this is a prohibited bribe because it involves taking someone else's turn and denying them their right to precedence.
A bribe means paying money in return for taking something to which one is not entitled or denying someone his due rights.
Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet, sallallahu ‘alayhi wa sallam, cursed the one who bribes and the one who takes bribes to influence the judgment. [Ahmad, Abu Daawood, An-Nasaa'i, At-Tirmithi and Ibn Maajah - At-Tirmithi graded it Hasan (good)] Moreover, ‘Umar, may Allah be pleased with him, reported that the Prophet, sallallahu ‘alayhi wa sallam, said, "The one who offers a bribe and the one who takes it are both in the Fire (of Hell)." [At-Tabaraani with a good chain of narration]
Allah knows best.