  We report the Griffiths phase (GP)-like state along with cluster-glass-like
state in geometrically frustrated antiferromagnetic $Cr$ substituted
$Y_2Ir_2O_7$ pyrochlore iridates. The strength of GP-like behaviour increases
with substitution. Interestingly, isothermal remanent magnetization suggests
the Ising-like interaction of spins in GP region. The GP-like state is not
attributed to the structural disorder as substitution of Cr does not induces
any structural change. Then the spin coupling between $Cr^{3+} \leftrightarrow
Cr^{3+}$, $Ir^{4+} \leftrightarrow Ir^{4+}$, $Ir^{4+} \leftrightarrow Cr^{3+}$
and $Ir^{4+} \leftrightarrow Ir^{5+}$ leads the competition between
antiferromagnetic and ferromagnetic correlations. It give rise to
Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction between $Cr^{3+}$ local
magnetic moments mediated by itinerant $Ir$ conduction electrons, hence, as a
result GP and cluster-glass-like states emerges.
