Hi there, I have a technical query about the linking of two paragraphs in an essay.

We all know that having connectivity in any two consecutive paragraphs is important, but does this rule apply to the whole of essay including the introduction and Final paragraphs as well?
e.g there is an essay on "Education" and after the introductory paragraph, I want to have a paragraph to define and elucidate the term "education", do I need to connect the introduction to the following paragraph as well? or can I keep the introduction separate and start a completely new paragraph?

Same goes for the Ending paragraph, do I need to keep it connected to the previous paragraph, or being the summarizing and final paragraph we can keep it as separate and non-connected?

Secondly, I have a specific case related to the same paragraph linking and I would like to ask about it as well. Kindly check the example below, where there is end of one paragraph and start of another, kindly see and let me know if these two paragraph would be considered as connected paragraphs?

"...but before we jump into the educational conditions of Pakistan, we need to define the term 'education' for a better understanding.
Education, means blah blah blah...."


Thanks!