Question

may be something like

template <class C>
struct apply<template<> struct T<C N>>
{
    typedef typename T<N + 1>::type type;
};

just for example it returns next integral constant type.

Answer 1

For any fixed type you can specialize directly:

template <typename> struct apply;  // primary template

template <unsigned int N>
struct apply<int_<N>>
{
    typedef int_<N + 1> type;
};

You can also specialize on templates that take one integer parameter:

template <template <unsigned int> class TInt, unsigned int N>
struct apply<TInt<N>>
{
    typedef TInt<N + 1> type;
};

The latter will match any template <unsigned int> class, though, so be careful.