He signed for Newport in July 2015 after the 34-year-old centre-half had been released by Cheltenham Town.
An experienced defender, Taylor has previously turned out for Charlton Athletic, Exeter City, Cheltenham and Bradford City in the Football League after spells in non-League football with the likes of Burscough, Rossendale United, Matlock Town, Hucknall Town, Halifax Town and Guiseley AFC.
He made his debut for County as a late substitute in a 1-0 victory away at Carlisle United towards the end of September.
But he made just four other appearances for the club, the most recent coming in the Emirates FA Cup home tie against Blackburn Rovers.
However, in total, he has more than 200 Football League appearances under his belt.