Praise be to Allah.
It is prescribed to make up the regular Sunnah prayers (al-sunan al-rawaatib) if they are missed because of an excuse such as sleeping, forgetting or being too busy to do them, which led to one not offering them at the proper time. So they may be made up even at times when prayer is not allowed, according to the correct scholarly opinion. That is because of the report narrated by al-Bukhaari (1233) and Muslim (834) from Umm Salamah (may Allah be pleased with her), according to which the Prophet (blessings and peace of Allah be upon him) prayed two rak‘ahs after ‘Asr; she asked him about that and he said, “Some people from ‘Abd al-Qays came to me and distracted me from offering the two rak‘ahs that come after Zuhr, so these are they.”
And Ibn Maajah (1154) narrated that Qays ibn ‘Amr said: The Prophet (blessings and peace of Allah be upon him) saw a man praying two rak‘ahs after Fajr. The Prophet (blessings and peace of Allah be upon him) said: “Fajr prayer twice?” The man said to him: I did not pray the two rak‘ahs that come before it, so I prayed them (now). And the Prophet (blessings and peace of Allah be upon him) did not say anything. Classed as saheeh by al-Albaani in Saheeh Ibn Maajah, 948.
And al-Tirmidhi (426) narrated from ‘Aa’ishah (may Allah be pleased with her) that if the Prophet (blessings and peace of Allah be upon him) did not pray four rak‘ahs before Zuhr, he would pray them afterwards. Classed as hasan by al-Albaani in Saheeh al-Tirmidhi.
Al-Nawawi (may Allah have mercy on him) said:
The correct view is our opinion is that it is mustahabb to make up the regular Sunnah prayers (al-sunan al-rawaatib). This is the view of Muhammad, al-Muzani, and Ahmad according to one report. Abu Haneefah, Maalik and Abu Yoosuf, according to the more well-known report from them, said: They should not be made up; our evidence is these saheeh hadeeths. End quote. al-Majmoo‘, 4/43
Al-Mardaawi al-Hanbali (may Allah have mercy on him) said:
The words “and whoever misses any of these Sunnah prayers, it is prescribed for him to make them up”– this is our madhhab (the madhhab of Imam Ahmad) and is the well known view according to our companions. End quote. al-Insaaf, 2/187
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
If one of the regular Sunnah prayers, such as the Sunnah prayer of Zuhr, is missed, can it be made up after ‘Asr? There are two views both of which were narrated from Ahmad. One of them is that it may not be made up; this is the view of Abu Haneefah and Maalik. The other view is that it may be made up. This is the view of al-Shaafa‘i and it is stronger. And Allah knows best. End quote. Majmoo‘ al-Fataawa, 23/127
Based on the above, if you are not able to offer the regular Sunnah prayers before and after Zuhr at the proper time, it is prescribed for you to offer them after ‘Asr.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: Is it permissible to delay the Sunnah prayer that is offered before Zuhr, as we start Zuhr prayer, then after approximately one hour we offer the Sunnah prayers that come before and after, because the time allowed for us to pray where we are studying outside the Kingdom is only enough to do wudoo’ and offer the (obligatory) prayer only?
If a person delays the Sunnah prayer that should be offered before until after the prayer, if that is because of an excuse then there is nothing wrong with him making it up later on, and it is acceptable. But if he had no excuse, then it is not acceptable. What the questioner has mentioned about the time only being enough to do wudoo’ and offer the obligatory prayer is an excuse; based on that, it is permissible to make up the Sunnah prayer that should come before after the prayer, but in this case one should start with the Sunnah that comes after the obligatory prayer, then make up the Sunnah that comes before. End quote. Fataawa wa Rasaa’il Ibn ‘Uthaymeen, 14/194
For more information please see the answer to question no. 114233.
And Allah knows best.