The Five-hundred-meter Aperture Spherical radio Telescope (FAST) has discovered more than 650 new pulsars, which account for 20% of our known Galactic pulsar population. In this paper, we estimate the prospect of a pulsar survey with a radio telescope array to be planned—the FAST Array (FASTA), consists of six "FAST-type" telescopes. Such a sensitive radio telescope array would be a powerful instrument in probing the pulsar population deep into our Galaxy as well as in nearby galaxies. We simulate the FASTA pulsar discovery prospects with different Galactic pulsar population models and instrumental parameter combinations. We find that FASTA could detect tens of thousands of canonical pulsars and well-over thousands of millisecond pulsars. We also estimate the potential yield if the FASTA is used to search for pulsars from the nearby spiral galaxy M31, and find that it would probably discover around a hundred new radio pulsars.