  Single crystals of Cu$_3$Bi(SeO$_3$)$_2$O$_2$Cl were investigated using
high-resolution capacitance dilatometry in magnetic fields up to 15 T.
Pronounced magnetoelastic coupling is found upon evolution of long-range
antiferromagnetic order at T$_{\mathrm{N}} = 26.4(3)$ K. Gr\"{u}neisen analysis
reveals moderate effects of uniaxial pressure on T$_{\mathrm{N}}$, of $1.8(4)$
K/GPa, $-0.62(15)$ K/GPa and $0.33(10)$ K/GPa for $p \parallel a$, $b$, and
$c$, respectively. Below 22 K, Gr\"{u}neisen scaling fails which implies the
presence of competing interactions. The structural phase transition at
T$_{\mathrm{S}} = 120.7(5)$ K is much more sensitive to uniaxial pressure than
T$_{\mathrm{N}}$, with strong effects of up to $27(3)$ K/GPa ($p \parallel c$).
Magnetostriction and magnetization measurements reveal a linear magnetoelastic
coupling for $B\parallel c$ below T$_{\mathrm{N}}$, as well as a mixed phase
behavior above the tricritical point around 0.4 T. An analysis of the critical
behavior in zero-field points to three-dimensional (3D) Ising-like magnetic
ordering. In addition, the magnetic phase diagrams for fields along the main
crystalline axes are reported.
