Let
\(\{X_i, i\ge 1\}\) be i.i.d.
\(\mathbb {R}^d\)-valued random vectors attracted to operator semi-stable laws and write
\(S_n=\sum _{i=1}^{n}X_i\). This paper investigates precise large deviations for both the partial sums
\(S_n\) and the random sums
\(S_{N(t)}\), where
N(
t) is a counting process independent of the sequence
\(\{X_i, i\ge 1\}\). In particular, we show for all unit vectors
\(\theta \) the asymptotics
$$\begin{aligned} {\mathbb P}(|\langle S_n,\theta \rangle |>x)\sim n{\mathbb P}(|\langle X,\theta \rangle |>x) \end{aligned}$$
which holds uniformly for
x-region
\(\gamma _n, \infty )\), where
\(\langle \cdot , \cdot \rangle \) is the standard inner product on
\(\mathbb {R}^d\) and
\(\{\gamma _n\}\) is some monotone sequence of positive numbers. As applications, the precise large deviations for random sums of real-valued random variables with regularly varying tails and
\(\mathbb {R}^d\)-valued random vectors with weakly negatively associated occurrences are proposed. The obtained results improve some related classical ones.