  We construct the four-derivative supersymmetric extension of $(1,0), 6D$
supergravity coupled to Yang-Mills and hypermultiplets. The hypermultiplet
scalars are taken to parametrize the quaternionic projective space
$Hp(n)=Sp(n,1)/Sp(n)\times Sp(1)_R$. The hyperscalar kinetic term is not
deformed, and the quaternionic K\"ahler structure and symmetries of $Hp(n)$ are
preserved. The result is a three parameter Lagrangian supersymmetric up to
first order in these parameters. Considering the case of $Hp(1)$ we compare our
result with that obtained from the compactification of $10D$ heterotic
supergravity on four-torus, consistently truncated to $N=(1,0)$, in which the
hyperscalars parametrize $SO(4,1)/SO(4)$. We find that depending on how $Sp(1)
\subset Sp(1,1)$ is embedded in $SO(4)$, the results agree for a specific value
of the parameter that governs the higher derivative hypermultiplet couplings.
