  The possibility of cluster emission from trans-lead (86$\leq$Z$\leq$96)
region of periodic chart has been explored comprehensively by employing few
empirical formulas which are modified by adding angular momentum ($l$) or
isospin-dependent ($I=(N-Z)/A$) or both terms for the calculation of cluster
decay half-lives. These modified versions of the formulas are found with lesser
${\chi}^2$ per degree of freedom and root mean-square error, in addition to the
smaller values of some other statistical parameters, while compared to their
corresponding old versions on available 61 experimental data of cluster
radioactivity. By applying the modified version of the formula given by
Balasubramaniam \textit{et al.} [PRC 70 (2004) 017301], the most accurate
formula among these, half-lives of several clusters i.e. isotopes of Be, B, C,
N, O, F, Ne, Na, Mg, and Si are predicted systematically for the several
isotopes in the trans-lead region. The contest of cluster emission with
$\alpha$-decay has been investigated in form of branching ratio which brings
several potential cluster emissions into the probable decay modes of these
nuclei. The accurate prediction of half-lives of such clusters is expected to
be crucial for the future experimental observations where $\alpha$-decay is
observed dominantly.
