No Objection Certificate (NOC) has been issued to you to appear in Indian Civil Services conducted by UPSC. On the basis of this NOC, you can apply for leave on the days of examination.
But on the basis of NOC, you can't apply for long-term study leave for Civil Services Examination, You can apply for leave, but your controlling officer has every right not to recommend the same.
Leave of a Central Government employee is governed by CCS (Leave) Rules, 1972. Please refer to Section 7(1) of the CCS (Leave) Rules which specifically states that: "Leave cannot be claimed as of right.'' Section 7(2) of CCS (Leave) Rules further stipulates that: "When the exigencies of public service so require, leave of any kind may be refused or revoked by the authority competent to grant it, but it shall not be open to that authority to alter the kind of leave due and applied for except at the written request of the Government servant''.
Your application for study leave will be governed by Section 7 of Leave Rules as mentioned above. However, I must add that except in cases of extreme emergency, leave is generally granted in such cases of UPSC examination preparation.
"If you are killed in action, you go to Heaven. If you win, you rule this Earth (as beautiful as Heaven). That is why, O son of Kunti, take a firm resolve and fight!"-- Shrimad Bhagwad Gita