What is the name of this Monad Stack function?

Question

I've got a bunch of stateful functions inside a State monad. At one point in the program there needs to be some IO actions so I've wrapped IO inside a StateT getting a pair of types like this:

mostfunctions :: State Sometype a
toplevel :: StateT Sometype IO a

To keep things simple I don't want pass the IO context into the main set of functions and I would like to avoid wrapping them in the monad stack type. But in order to call them from the toplevel function I need something akin to a lift, but I'm not trying to lift a value from the inner monad. Rather I want to convert the state in the StateT monad into something equivalent in the State monad. To do this I've got the following:

wrapST :: (State Sometype a) -> StateT Sometype IO a
wrapST f = do s <- get
              let (r,s2) = runState f s 
              put s2
              return r

This then get used to interleave things like the following:

toplevel = do liftIO $ Some IO functions
              wrapST $ Some state mutations
              liftIO $ More IO functions
              ....

It seems like a fairly obvious block of code so I'm wondering does this function have a standard name, and it is already implemented somewhere in the standard libraries? I've tried to keep the description simple but obviously this extends to pulling one transformer out of a stack, converting the wrapped value to the cousin of the transformer type, skipping the monads below in the stack, and then pushing the results back in at the end.