  In this contribution we study the asymptotics of \begin{eqnarray*} P(\exists
t\ge 0 : B_H(L(t))-cL(t)>u), \quad u \to \infty, \end{eqnarray*} where $B_H,
H\in (0,1)$ is a fractional Brownian motion, $L(t)$ is a non-negative pure
jumps L\'{e}vy process independent of $B_H$, $c>0$.
