The reaction: HI + Cl --> HCl + I Predict whether it will be exothermic or endothermic and why.?

As written, your reaction must be a free radical exchange of I for Cl, meaning that the H-Halogen bond breaking and forming is "homolytic"; that is each species is uncharged:

H-X → H· + X·

Homolytic bond strengths will decrease going down the periodic table. That means it will take more energy to break an H-Cl bond homolytically than to break an H-I bond; so conversely, it will give more energy to form an H-Cl bond homolytically than to form an H-I bond. Therefore the reaction is exothermic as written.
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