  Let $K$ be an NIP field and let $v$ be a henselian valuation on $K$. We ask
whether $(K,v)$ is NIP as a valued field. By a result of Shelah, we know that
if $v$ is externally definable, then $(K,v)$ is NIP. Using the definability of
the canonical $p$-henselian valuation, we show that whenever the residue field
of $v$ is not separably closed, then $v$ is externally definable. In the case
of separably closed residue field, we show that $(K,v)$ is NIP as a pure valued
field.
