The chaser and the chased can offer Salat (prayer) while riding , and by signs
حَدَّثَنَا عَبْدُ اللَّهِ بْنُ مُحَمَّدِ بْنِ أَسْمَاءَ، قَالَ حَدَّثَنَا جُوَيْرِيَةُ، عَنْ نَافِعٍ، عَنِ ابْنِ عُمَرَ، قَالَ قَالَ النَّبِيُّ صلى الله عليه وسلم لَنَا لَمَّا رَجَعَ مِنَ الأَحْزَابِ " لاَ يُصَلِّيَنَّ أَحَدٌ الْعَصْرَ إِلاَّ فِي بَنِي قُرَيْظَةَ ". فَأَدْرَكَ بَعْضُهُمُ الْعَصْرَ فِي الطَّرِيقِ فَقَالَ بَعْضُهُمْ لاَ نُصَلِّي حَتَّى نَأْتِيَهَا، وَقَالَ بَعْضُهُمْ بَلْ نُصَلِّي لَمْ يُرَدْ مِنَّا ذَلِكَ. فَذُكِرَ لِلنَّبِيِّ صلى الله عليه وسلم فَلَمْ يُعَنِّفْ وَاحِدًا مِنْهُمْ.
Narrated Ibn `Umar: When the Prophet (ﷺ) returned from the battle of Al-Ahzab (The confederates), he said to us, "None should offer the 'Asr prayer but at Bani Quraiza." The 'Asr prayer became due for some of them on the way. Some of them decided not to offer the Salat but at Bani Quraiza while others decided to offer the Salat on the spot and said that the intention of the Prophet (ﷺ) was not what the former party had understood. And when that was told to the Prophet (ﷺ) he did not blame anyone of them.