Making up the Sunnah prayer that is done before Zuhr

Firstly: 

It is mustahabb to make up the regular Sunnah prayers if one misses them, according to the correct scholarly view. This is the Shaafa’i view and the well known opinion of the Hanbalis, in contrast to the Hanafis and Maalikis, because of the hadith of Umm Salamah (may Allah be pleased with her), according to which the Prophet (peace and blessings of Allah be upon him) prayed two rak’ahs after ‘Asr. He was asked about them and he said: “O daughter of Abu Umayyah, you asked about the two rak’ahs after ‘Asr. That is because some people from ‘Abd al-Qays came to me and distracted me from the two rak'ahs that come after Zuhr; these are they (i.e., I prayed them just now).” Narrated by al-Bukhari (1233) and Muslim (834). 

Imam al-Nawawi (may Allah have mercy on him) said: 

The correct view in our opinion is that it is mustahabb to make up the regular naafil prayers. This was the view of Muhammad, al-Muzani and Ahmad according to one opinion narrated from him. Abu Haneefah, Maalik and Abu Yoosuf, according to the most well known view narrated from him, said that they should not be made up. Our evidence is these saheeh ahadith. End quote. 

Al-Majmoo’ (4/43). 

Al-Mardaawi al-Hanbali (may Allah have mercy on him) said: The words “whoever misses any of these Sunnahs, it is Sunnah for him to make it up” – this is the well known view of our companions. 

Al-Majd supported this in his commentary and it was the view favoured by Shaykh Taqiy al-Deen – i.e., Ibn Taymiyah. End quote from al-Insaaf (2/187). 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

Making up regular Sunnah prayers is Sunnah if one misses them. The evidence for that is that when the Prophet (peace and blessings of Allah be upon him) slept and missed Fajr prayer, and did not wake up until after the sun had risen, he prayed the Sunnah prayer of Fajr first, then he prayed Fajr after that. End quote. 

Liqaa’aat al-Baab il-Maftooh (no. 74, question no 18). See also al-Mawsoo’ah al-Fiqhiyyah (25/284). 

Secondly: 

If he wants to make up the Sunnah prayer that comes before Zuhr after offering the fard Zuhr prayer, should he pray the Sunnah prayer that comes before Zuhr first, and then the Sunnah prayer that comes after Zuhr, or vice versa? 

It seems that this matter is broad in scope, whether he starts with the Sunnah prayer that comes before or that which comes after, because what matters is doing it, whether it is done sooner or later. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

The scholars said: If you miss the two rak’ahs that come before Zuhr, then pray them after the prayer, because you were excused from doing them before the prayer. This happens all the time: a person comes to the mosque and finds that they have already started the prayer. In this case, he should make them up after he prays Zuhr. 

But he should offer the regular Sunnah prayer that comes after Zuhr before the regular Sunnah prayer that comes before. 

A man comes and the people are praying, and he is not able to offer the Sunnah prayer of Zuhr. When he has prayed Zuhr, he should pray two rak'ahs with the intention of offering the regular Sunnah prayer that comes after Zuhr, then make up the regular sunnah prayer that comes before. This was narrated from the Prophet (peace and blessings of Allah be upon him) in a hadith narrated by Ibn Majaah. 

Fath Dhi’l-Jalaal wa’l-Ikraam bi Sharhh Buloogh al-Maraam (2/225). 

And Allah knows best.