 Relative extension of a compatible almost complex structure

If a compatible almost complex structure is prescribed along a closed symplectic submanifold $N\subset M$ and preserves $TN$, it extends to one on $M$. Choose a compatible structure separately on $TN$ and its symplectic normal bundle, use the associated metric along $N$, extend that metric to $M$, and apply the metric construction of a compatible almost complex structure.