Dempsey, 32, has represented a range of clubs throughout his career, including FC United of Manchester, Farsley Celtic and Bradford Park Avenue.
He most recently featured for Yorkshire Amater, prior to his departure in April.
Dempsey previously played at junior level with Bradford City and Sheffield United and also spent time at the Glenn Hoddle Academy.
Meanwhile, midfielder Proctor has also penned terms at the Clayborn ahead of the 2022/23 season.
The duo will join Sedge as they prepare to compete in the Pitching In NPL Premier Division following their promotion from Step 4.
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