A combinator expression (let's say in the SK basis) can be thought of as a function that maps combinator calculus expressions to combinator calculus expressions. That is, one can think of an expression $X$ as a function $X:L \to L$, where $L$ is the set of all syntactically valid combinator expressions in the SK basis. This mapping is performed by applying the input to the expression, and then reducing to normal form to get the output.
Since the SK basis is Turing complete, one might naïvely think that there exists a an SK expression $X$ that implements any computable function from $L$ to $L$. However, this clearly isn't the case, since the result of reduction will always be in normal form. This means there is no way for an expression to have an output that isn't in normal form.
So instead, I could think of SK calculus expressions as mapping $L'$ to $L'$, where $L'$ is the set of SK expressions in normal form. Is it the case that, for any computable map $f:L'\to L'$, there is an SK expression $X$ that implements this map? Or are there further restrictions on the set of functions that can be computed by combinator calculus expressions in this way?