The assembly of a DNA-DNA polymerase binary complex is the precursory step in genome replication, in which the enzyme binds to the 3' junction created when a primer binds to its complementary substrate. In this study, we use an active control method for observing the binding interaction between Klenow fragment (exo-) (KF) in the bulk-phase chamber above an α-hemolysin (α-HL) nanopore and a single DNA molecule tethered noncovalently in the nanopore. Specifically, the control method regulates the temporal availability of the primer-template DNA to KF binding and unbinding above the nanopore, on millisecond-to-second time scales. Our nanopore measurements support a model that incorporates two mutually exclusive binding states of KF to DNA at the primer-template junction site, termed "weakly bound" and "strongly bound" states. The composite binding affinity constant, the equilibrium constant between the weak and strong states, and the unbound-to-strong association rate are quantified from the data using derived modeling analysis. The results support that the strong state is in the nucleotide incorporation pathway, consistent with other nanopore assays. Surprisingly, the measured unbound-to-strong association process does not fit a model that admits binding of only free (unbound) KF to the tethered DNA but does fit an association rate that is proportional to the total (unbound and DNA-bound) KF concentration in the chamber above the nanopore. Our method provides a tool for measuring pre-equilibrium kinetics one molecule at a time, serially and for tens of thousands of single-molecule events, and can be used for other polynucleotide-binding enzymes.