  The hole doped Fe-based superconductors Ba$_{1-x}$A$_x$Fe$_2$As$_2$ (where
A=Na or K) show a particular rich phase diagram. It was observed that an
intermediate re-entrant tetragonal phase forms within the orthorhombic
antiferromagnetically-ordered stripe-type spin density wave state above the
superconducting transition [S. Avci et al., Nature Comm. 5, 3845 (2014), A. E.
B\"ohmer et al., arXiv:1412.7038v2]. A similar intermediate phase was reported
to appear if pressure is applied to underdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ [E.
Hassinger et al., Phys. Rev. B 86, 140502(R) (2012)]. Here we report data of
the electric resistivity, Hall effect, specific heat, and the thermoelectrical
Nernst and Seebeck coefficients measured on a Ba$_{0.85}$K$_{0.15}$Fe$_2$As$_2$
single crystal under pressure up to 5.5 GPa. The data reveals a coexistence of
the intermediate phase with filamentary superconductivity. The Nernst
coefficient shows a large signature of nematic order that coincides with the
stripe-type spin density wave state up to optimal pressure. In the
pressure-induced intermediate phase the nematic order is removed, thus
confirming that its nature is a re-entrant tetragonal phase.
