The 22-year-old has agreed a one-month deal and is likely to come into the Hamlet squad tomorrow as they face Wealdstone at home in the league.
Nash is in the second of a two-year deal with the Gills but has made just two league starts.
Nash joined the Gills last summer from Bostik League North side Maldon & Tiptree on a two-year contract and has since made 15 appearances for the club.
He had a productive spell on loan at Bostik Premier side Leatherhead last season, scoring 5 times in 8 league outings before returning to Priestfield for the remainder of the 2017/18 campaign.
However, he has only made one appearance for Gills this season, that being in Tuesday’s 4-0 defeat at Portsmouth in the Checkatrade Trophy.
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