Sheikh `Abd al-Rahmân al-`Ajlân, lecturer at the Grand Mosque in Mecca
It is encouraged for a Muslim to beseech Allah in supplication at all times. Allah says: “And when My servants ask you concerning Me, then surely I am very near; I answer the prayer of the suppliant when he calls on Me.” [Sûrah al-Baqarah: 186]
This is especially true at the times when supplications are most readily answered. These times include the interval between the adhân and the iqâmah, the last third of the night, the last hour before sunset on Friday, and when it rains. These and other times are mentioned in the Sunnah.
With respect to the five obligatory prayers, the scholars have determined that it is not best to supplicate immediately thereafter. This is because there is something else which is strongly encouraged for us to engage in at that time – the prescribed remembrances. It is not recommended for the worshipper to busy himself with something else – even something that is good in and of itself – at the expense of a prescribed Sunnah.
With respect to the time after completing a voluntary prayer, there is nothing specifically mentioned in the Sunnah to recommend it as a time to single out for supplications. Therefore, we should not treat it as a special time to set aside for our supplications.
However, the time after one makes the taslîm form a voluntary prayer is just like any other time. A person is free to supplicate at this time as the inclination takes him. Supplication is a generally encouraged form of worship.
And Allah knows best.
Source: Islam Today