In the name of Allah, Most Beneficent, Most Merciful
Thank you for your query. May Allah enable us to be punctual and particular about our 5 daily prayers.
If a person completes one unit of prayer (raka’ah) during the prescribed time, the entire prayer is ada (on time). If this is not the case, the prayer will be considered qada (having been prayed out of its time).
The Prophet (Allah bless him and give him peace) has said:
من أدرك ركعة من الصلاة فقد أدرك الصلاة
Whoever has attained a (raka’ah) of the prayer, he has indeed attained the prayer i.e. in its time (Bukhari, hadith 580).
Application of the above:
Your question indicates that you completed one unit of prayer for dhur and thereafter the opening takbir for asr was given. The opening takbir for a given prayer is normally given after the call to prayer and the sunan (supererogatory prayers preceding the fard) have been performed.
If this is indeed the case, then your prayer is qada and not ada. Alternatively, if you have completed one unit of prayer and then the adhan (denoting the entrance of the time) for asr is called out, then your prayer will be considered ada (al-Manhaj al-qawim 182).
The most beloved action to Allah is to offer the prayers at their earliest fixed times. Do keep in mind and heart the verse of the Qur’an: Indeed, performing prayers is a duty on the believers at the appointed times (Qur’an 4:103).
All the very best
In the care of Allah
[Shaykh] Muhammad Carr
Checked and Approved by Shaykh Faraz Rabbani