  Jets constructed via clustering algorithms (e.g., anti-$k_T$, soft-drop) have
been proposed for many precision measurements, such as the strong coupling
$\alpha_s$ and the nucleon intrinsic dynamics. However, the theoretical
accuracy is affected by missing QCD corrections at higher orders for the jet
functions in the associated factorization theorems. Their calculation is
complicated by the jet clustering procedure. In this work, we propose a method
to evaluate jet functions at higher orders in QCD. The calculation involves the
phase space sector decomposition with suitable soft subtractions. As a concrete
example, we present the quark-jet function using the anti-$k_T$ algorithm with
E-scheme recombination at next-to-next-to-leading order.
