Can I switch from a variable closed mortgage to fixed rate mortgage?

Yes. You can move from a variable closed mortgage to a fixed rate mortgage before your term ends, as long as the new term is equal to or longer than the time remaining on your current term. 
For example, if you have a 5-year variable closed mortgage and want to switch to a fixed rate after 2 years, you could choose a 3-,4-or 5-year fixed term.