This concept is important so it gets its own page:

• You need a topic sentence for each unit of support in an essay.
• Units of support may consist of more than one paragraph.
• So each paragraph does not need a topic sentence.
• However, each unit of support requires a topic sentence.

Here’s an example:

You’ve written a thesis about the physical, psychological, and social effects of the opioid crisis.  Given the thesis, you know you’ll need at least three topic sentences, one for each effect.  However, there may be many physical, psychological, and social effects, more than are feasible to deal with in one paragraph per effect.  Additional paragraphs for each effect may not need their own topic sentences, as the topic sentence for that unit of support serves as the overall idea for that section of the essay.

Note that I said “may” in the sentence above.  If it makes sense to do smaller topic sentences, especially for a complicated or very sophisticated topic sentence idea, you may do so.  But understand that one topic sentence per unit of support is absolutely fine, in the interest of clarity and conciseness. It may help to think of topic sentences and units of support in terms of a pie chart.  Not every unit of support is an equal slice of the pie – some are larger and some are smaller.  The larger slices are units of support that may have more than one paragraph per topic sentence.