Both are misinterpretations of statistical independence. They both deal with erroneous beliefs about sequences of independent or nearly independent events. The belief that independent, random events are influenced by past outcomes.
Gambler's Fallacy is about expecting a reversal in a pattern, while the hot-hand fallacy involves expecting a continuation of a pattern.
They're related in that they both deal with erroneous beliefs about sequences of independent or nearly independent events. For example, thinking a flipped coin is "due" for heads after several tails. This is a cognitive error; each coin flip is independent with a 50/50 chance. The fallacy is a misunderstanding of statistical independence and the law of large numbers.
The hot-hand fallacy is the opposite belief to Gambler's Fallacy: the conviction that a streak of successful outcomes increases the probability of future success. For example, basketball betters see certain players get the “hot-hand,” believing a basketball player who has made several shots will continue to do so, even when they are actually seeing lucky streaks that are consistent with the player’s typical scoring percentage.