You can change

    appV fn x = atomically $ readTVar x >>= writeTVar x . fn

to

    appV fn x = atomically $ modifyTVar x fn

The function getValue need not be in IO monad. You can simplify it using fromMaybe in Data.Maybe.

Sometimes you check "head l" and "tail l"; it's more idiomatic to use pattern matching. For example, you can change:

    setCommand handle cmd db = do
        appV (conv k v) db
        hPutStrLn handle $ "OK"
        where k = (head cmd)
              v = (unwords (tail cmd))
    ....
    case (head cmd) of
        ("get") -> getCommand handle (unwords (tail cmd)) db
        ("set") -> setCommand handle (tail cmd) db

to something like this:

    setCommand handle key val db = do
        appV (conv key val) db
        hPutStrLn handle "OK"
    ...
    case cmd of
      "get":key     -> getCommand handle (unwords key) db
      "set":key:val -> setCommand handle key (unwords val) db

Also consider using hlint, it often gives good advice.