Was there a hyperinflation after the deflation during the Great Depression?
No.
Was there a hyperinflation after the deflation in post-bubble 90's Japan?
No. In fact Japan has almost been in deflation ever since.
There was also a deflation in Hong Kong following the 1997 Asian financial crisis, which lasted until 2004. AFAIK, there was not any particularly noteworthy hyperinflation which followed, aside from the standard inflation the world saw over the past few years until recently.
There were 3 other noteworthy periods of deflation:
One in the US following the Civil War (after the US went back on the gold standard, having temporarily abandoned it during the war). This deflation lasted some 25 years. AFAIK there was no particular hyperinflation in the US in the early 1900's after the deflationary period ended.
The second was in the US which followed the recession of 1836. AFAIK there was no hyperinflation afterwards.
Finally there was one in the UK after WWI, which existed for similar reasons as the post-Civil War deflation (the UK temporarily went off the gold standard during the war, then returned to it afterwards, creating deflation).
One might say that the deflations prior to ~1971 "don't count" because the nations which experienced them were on (or went back to) the gold standard. But even ignoring those, we still have the deflations in Japan and Hong Kong, neither of which were followed by periods of hyperinflation.
So the answer to your question is, Not necessarily. Of course there could be a first time, but historically there has been no reason for it.
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Wiki article on deflation <--