Can I pray after Fajr?

It depends what you mean to pray. Between the entry of Fajr and sunrise you pray the Fajr prayer itself, its two rakʿahs of sunnah, any missed prayers (in the Ḥanafī view), and the funeral prayer. What is withheld is other voluntary prayer: from the entry of Fajr, nafl is suspended until the sun has not only risen but climbed for about twenty minutes. In the Shāfiʿī school, voluntary prayers that have a specific cause, such as greeting the mosque, remain valid even then. The answer below is conditioned on exactly what you intend to pray.

Rulings differ by madhhab and by what you intend to pray - the live answer below is conditioned on both. Draft pending scholar verification; see the methodology.