What kind of system is required for dynamic equilibrium to be set up?
If energy can be transferred, it does not mean it is transferred. 

If there is e.g. zero net thermal energy transfer, a system is in thermal equilibrium with the neighborhood, even if it is not isolated.

As Ivan says, an equilibrium is possible even in an open system, if net transfer of particular matter kinds is zero.

The thermodynamic equilibrium consists of thermal, radiative, chemical and mechanical equilibrium.

Note that thermodynamic equilibrium happens at following conditions:


  
  For a completely isolated system, the entropy $S$ is maximum at thermodynamic equilibrium.
  For a system with controlled constant temperature and volume, the Helmholtz free energy $A$ is minimum at thermodynamic equilibrium.
  For a system with controlled constant temperature and pressure, the Gibbs free energy $G$ is minimum at thermodynamic equilibrium. 
  


$$\begin{align}
G&amp;=H-TS \\
\Delta G&amp;=\Delta H-T\Delta S \\
\end{align}$$

Total entropy of the not isolated system and it's surrounding increases in time. 

Entropy of the system alone may decrease with time, if the Gibbs energy of system decreases, as this latter decrease also means 
$$\Delta S_{\rm surrounding} +  \Delta S_{\rm system}  \gt 0$$