Interacting selectively and non-covalently with a specific transcription factor, which may be a single protein or a complex, and with another protein, macromolecule, or complex, recruiting that specific transcription factor to the transcription machinery complex and thus permitting those molecules to function in a coordinated way, in order to modulate transcription. A protein binding transcription factor may or may not also interact with the template nucleic acid (either DNA or RNA) as well.