  For any odd $t\ge 9$, we present a polynomial-time algorithm that solves the
$3$-colouring problem, and finds a $3$-colouring if one exists, in $P_{t}$-free
graphs of odd girth at least $t-2$. In particular, our algorithm works for
$(P_9, C_3, C_5)$-free graphs, thus making progress towards determining the
complexity of $3$-colouring in $P_t$-free graphs, which is open for $t\ge 8$.
