Zikr after the Fardh and Sunnah prayers
In the name of Allah, the most Beneficent, the most Merciful.
Saaiduna Abdullah Ibn Abbas Radiallahu Anhu narrates that the raising of the voice of the zikr was practiced in the time of the Prophet of Allah Sallallahu Alahi Wasalam when they left the obligatory prayer. And Ibn Abbas Radiallahu Anhu said “I would know of when people left the obligatory prayer by the (loud) zikr and I used to hear it.” (Sunan Abi Dawud p.150 v.1)
From the above narration we can establish that it is permissible to recite the various forms of zikr, tasbih and dua after the fardh prayers. However, it is the sunnah of the Prophet of Allah Sallallahu Alahi Wasalam to rise for the sunnah payer straight away and link it to the obligatory prayer with the exception that it is recommended to separate a moment between them as Saaidah Aaisha Radiallahu Anha reports that the Prophet of Allah Sallallahu Alahi Wasalam would wait the amount of time it took to recite ‘O Allah, Thou are Peace, and Peace comes from Thee, Blessed You are, O Possessor of glory and honour’, thereafter he would stand for the sunnah prayer. (Sunan Abi Dawud)
Shamsul Aaimmah Al Halwany (RA) said, “There is no harm in reciting invocations between the obligatory and sunnah prayer.” However, in Al Ikhtiyar it is stated that every prayer that is followed by a sunnah is disliked to sit and supplicate for. (Nurul Idah p.80 and Maraqi Falah p.116)
With regards to your question, it is not necessary that one be required to do the zikr and tasbih after the fardh prayers. Some scholars have permitted it also after the sunnah prayers. (See Fathul Qadir p.440 v.1, Ghunyah al Mutamalli P.344, Siayah p.257-260 v.2, Nahrul Faiq p.296 v.1 Bahrur Raiq p.35 v.2, Badai us Sanaai p.159 v.1)
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham.