  We study two integrable systems associated with the coupled NLS equation: the
integrable defect system and the integrable boundary systems. Regarding the
first one, we present a type I defect condition, which is described by a
B\"{a}cklund transformation frozen at the defect location. For the resulting
defect system, we prove its integrability both by showing the existence of an
infinite set of conserved quantities and by implementing the classical
$r$-matrix method. Regarding the second one, we present some new integrable
boundary conditions for the coupled NLS equation by imposing suitable
reductions on the defect conditions. Our new boundary conditions, unlike the
usual boundary conditions (such as the Robin boundary), involve time
derivatives of the coupled NLS fields and are characterised by non constant
$K(\lambda)$ matrices. We prove the integrability of our new boundary
conditions by using Sklyanin's approach.
