Virtue and times of regular Sunnah prayers (Sunnah mu’akkadah)
The regular Sunnah prayers fall into two categories:
Sunnahs which are done before the fard prayer – two rak’ahs before Fajr and four before Zuhr.
Sunnahs which are done after the fard prayer – two rak’ahs after Zuhr, two rak’ahs after Maghrib and two rak’ahs after ‘Isha’.
Concerning their virtue, it was narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever prays twelve rak’ahs during the night and day, a house will be built for him in Paradise: four before Zuhr and two after, two rak’ahs after Maghrib, two rak’ahs after ‘Isha’ and two rak’ahs before Fajr prayer.”
Narrated by al-Tirmidhi, no. 380; classed as saheeh by al-Albaani in Saheeh al-Jaami’, 6362.
The time for a Sunnah prayer that comes before a fard prayer is from the beginning of the time for that prayer, until the iqaamah.
The time for a Sunnah prayer that comes after a fard prayer is from after the salaam at the end of the fard prayer until the end of the time for that prayer.
Ibn Qudaamah (may Allaah have mercy on him) said: “The time for every Sunnah prayer that comes before a fard prayer is from the beginning of the time for that prayer, until the prayer is done, and the time for every Sunnah prayer that comes after a fard prayer is from after the prayer is done until the end of the time for that prayer.”
Al-Mughni, 2/544
Based on this, it is not correct to pray the Sunnah prayer before the time for the fard prayer begins, rather you should wait until the time for that prayer comes, then pray it.
See also Questions no. 1048, 4057
And Allaah knows best.