Catalysis of the reaction: a 1-phosphatidyl-1D-myo-inositol 4-phosphate + ATP = a 1-phosphatidyl-1D-myo-inositol 3,4-bisphosphate + ADP + H+.
ATP:1-phosphatidyl-1D-myo-inositol-4-phosphate 3-phosphotransferase activity