Moving to hierarchical design
Yes you can. One limitation that you must appreciate with KiCAD at the moment is that it only supports one sheet per hierarchical level Citation this includes the root level. 

You can have as many hierarchical blocks at a level that you wish (some #define limit somewhere)

The benefits of a hierarchical circuit is structure and also re-use such that if you have a block used multiple time (gatedrive) and you need to change part of it, you only need to change in one location. 

The downside is the navigation can become non-intuitive if the structure has organic growth. Consider re-sizing the sheet before embarking on a hierarchical system 

How to convert?
Consider this dummy cct: two cascaded salen-key. You want to convert to a hierarchical system for organisation, re-use or sheet space



I want a common 15.9kHz salen key.


create hierarchical sheet 

In this instance I am naming the sheet SalenKey.sch 
cut the circuit

Highlight the block with left-mouse and release (don't move mouse). Right-click and choose cut to cut the blocks to the clipboard
enter hierarchical block

Right-click on the block and click Enter Sheet
paste



Right-click (or Cntr-V) to paste the circuit into the sheet


connect hierarchical ports 


All the inputs and outs now need a hierarchical port. Equally if you are not using global power, power connections need ports. 

I personally like keeping these pins in the top-left and top-right and then using net names as this provides a clear context boundary for the sheet




Connect at root 
Push back to the root and now the hierarchical pins need to be placed onto the symbol 

click the place hierarchical pins icon and then click onto the hierarchical symbol. This will import each pin one at a time. Place on the left/right as you see fit. as for KiCAD-5.1 you cannot place on top/bottom (would be handy for power...)




 

Risize as you seem fit. Since I typically do this for re-use v(eg gatedrives), you can link multiple instances to one sheet simply by following #1 and naming the sch file exactly as the one you want to reuse