The definition of a competitive inhibitor is that it binds to the same enzyme form as the substrate. If the enzyme-substrate complex forms, this is no longer the same enzyme form, so if the inhibitor binds to the ES complex, it is not a competitive inhibitor. If the inhibitor binds to E, it doesn't have to bind to the active site. It can  bind to an allosteric site and still be a competitive inhibitor because substrate also binds to E.

To add a bit to Marcia Moss's answer, an inhibitor that binds selectively to the enzyme-substrate (ES) complex only is called an "uncompetitive" inhibitor. The binding site does not have to be separate from the active site. It could be within a part of the active site that is not occupied by the bound substrate. For example, consider the case of a two-substrate enzyme in which the active site has space for both substrates, but the inhibitor only binds after the first substrate has bound.

With all due respect to Marcia Moss and Adam Shapiro, my question just looked a simplified one thus requiring a textbook answers. In fact, while mentioning a kinetics of enzyme-substrate complex in the presence of “waiting to be called competitive inhibitor”, I expected enzymologists’ quick reply with reference to recent pioneer paper of Saha et al (J Chem Phys. 137(4):045102, 2012) entitled “Single-molecule enzyme kinetics in the presence of inhibitors”. As I consider this a significant input to enzymology completely applicable to my area of membrane-bound monooxygenases, let me, in truncated format, present  explanations of their findings: “Recent studies in single-molecule enzyme kinetics reveal that the turnover statistics of a single enzyme is governed by the waiting time distribution that decays as multi-exponential at high substrate concentration. The multi-exponentiality arises due to protein conformational fluctuations, which act on the time scale longer than or comparable to the catalytic reaction step, thereby inducing temporal fluctuations in the catalytic rate resulting in dynamic disorder. In this work, we study the turnover statistics of a single enzyme in the presence of inhibitors to show that the multi-exponentiality in the waiting time distribution can arise even when protein conformational fluctuations do not influence the catalytic rate. From the Michaelis-Menten mechanism of inhibited enzymes, we derive exact expressions for the waiting time distribution for competitive, uncompetitive, and mixed inhibitions to quantitatively show that the presence of inhibitors can induce dynamic disorder in all three modes of inhibitions resulting in temporal fluctuations in the reaction rate. In the presence of inhibitors, dynamic disorder arises due to transitions between active and inhibited states of enzymes, which occur on time scale longer than or comparable to the catalytic step. In this limit, the randomness parameter (dimensionless variance) is greater than unity indicating the presence of dynamic disorder in all three modes of inhibitions. In the opposite limit, when the time scale of the catalytic step is longer than the time scale of transitions between active and inhibited enzymatic states, the randomness parameter is unity, implying no dynamic disorder in the reaction pathway”.

Does this phenomenon relate in any way to the phenomenon of slow-binding or time-dependent inhibition? The treatment of such inhibitors supposes that enzymes can progress with a slow rate constant from an initial E.I encounter complex of relatively low affinity to a higher affinity E.I* state due to a conformational transition.