There isn't a standard field which is just a time picker.
You could create a "Select List (Single Choice)" field as an alternative - and list each time you want to set against an issue. It might work if it's just every hour or every 15-30 minutes, but I appreciate if you want the whole 24 hour clock this isn't feasible.
The other alternative is to look for a field or app which can do this on the Atlassian Marketplace.
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