Defender Josh Lacey joins after he was released by Scarborough on the eve of the season, alongside Alfreton Town midfielder Jordan Sinnott.
Lacey, 24, was signed by Kittrick for Scarborough from Gainsborough last summer, and soon made the right back spot his own.
Former Huddersfield junior Sinnott, 25, has played for Altrincham, Halifax and Chesterfield.
The Gladiators face Stafford Rangers on Saturday before welcoming Gainsborough Trinity on Bank Holiday Monday.
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