I know that it is Sunna to pray 4 Rak'at before Salat Al Asr, however can we pray them after the Eqama or must they be after the Azan and before the Eqama?
May Allah guide us all to that which is beneficial, ameen
Regarding your question; It is not recommended to start 'sunnah' prayers after the Iqamah (the call for prayer to commence) as there will be no time to do this because the obligatory prayers begin straight after the Iqamah. Therefore these prayers are to be done after the Adhaan and before the Iqamah.
However if one is already praying their sunnah prayers while the Iqamah is being given then the following advise and verdict of Al-Imam Muhammad Ibn Saalih al-Uthaymeen should be adhered to;
"If a person praying the sunnah while the iqamah is called, then the best opinion in this case is that if he is in his second rak‘ah, he should shorten it, and if he is in the first rak‘ah, he should just break his prayer and enter the congregation with the Imam. The evidence for this comes from what Imam Muslim has narrated in his Sahih:
Prophet (peace be upon him) said: If iqamah is called for the prayer then there is no prayer except the obligatory one.
(Sahih Muslim, 1/493)
So, if one has performed the ruku‘ for the second rak‘ah, then he should complete the prayer, and if not, then he should discontinue because what is left from his sujud and tashahhud is not needed any more. Moreover, he should break without salaam, and it is enough to have the intention in the heart, contrary to common misconception"
Majmu Fatawa Ibn Uthaymeen, volume 1 page 345
And Allah alone knows best.
May Allah bless you with much goodness, ameen.