Mediates the nuclear export of proteins (cargos), such as EIF5A, SMAD3 and isoform M2 of PKM (PKM2) (By similarity). In the nucleus binds cooperatively to its cargo and to the GTPase Ran in its active GTP-bound form (By similarity). Docking of this trimeric complex to the nuclear pore complex (NPC) is mediated through binding to nucleoporins (By similarity). Upon transit of a nuclear export complex into the cytoplasm, disassembling of the complex and hydrolysis of Ran-GTP to Ran-GDP (induced by RANBP1 and RANGAP1, respectively) cause release of the cargo from the export receptor (By similarity). XPO4 then return to the nuclear compartment and mediate another round of transport (By similarity). The directionality of nuclear export is thought to be conferred by an asymmetric distribution of the GTP- and GDP-bound forms of Ran between the cytoplasm and nucleus (By similarity). Catalyzes the nuclear export of hypusinated EIF5A; a small cytoplasmic protein that enters nucleus and accumulates within nucleolus if not exported back by XPO4 (PubMed:27306458). Specifically mediates nuclear export of isoform M2 of PKM (PKM2) following PKM2 deacetylation by SIRT6 (By similarity). Also mediates the nuclear import of SOX transcription factors SRY and SOX2 (PubMed:19349578). Interacts with Ran and cargo proteins in a GTP-dependent manner. Shuttles between the nucleus and the cytoplasm. Belongs to the exportin family.