We present a calculation of the renormalized HQET Lagrangian
at order O(1/m_Q^3) in the one particle sector.
The anomalous dimensions
of local operators and
time ordered products of dimension 7 contributing at this
order are calculated in the one loop approximation.
We show that a careful treatment of the time ordered
products is necessary to arrive at a gauge independent
renormalized lagrangian.
Our result sets the stage for an investigation of reparametrization
invariance at O(1/m_Q^3).
