Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is nothing wrong with making up the missed sunnah prayer as The Prophet (peace be upon him) has set a precedent.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Yes, you may make up sunnah prayers. The Prophet (peace be upon him) has set a precedent. Aishah, the beloved wife of the Prophet, reports that she saw the Prophet praying after Asr. On inquiring about it, he told her he was making up for the sunnah of Zhuhr — he had missed– because he was busy with an urgent business with a delegation who had come to visit him.
Based on this precedent, scholars have ruled that one may make up the missed Sunnah prayers one has missed.
Alternatively, one may also compensate for them by offering extra nafl prayers. There are no restrictions on performing them as long as one avoids the forbidden times, namely, the exact time of sunrise, when the sun is at the meridian, or when the sun is actually setting.
Almighty Allah knows best.