The 26-year-old has committed his immediate future to the League Two club after making 29 appearances in all competitions in the 2025-26 campaign.
Brennan proved a versatile figure for County by playing in various positions, including full-back, centre-back and midfield
The former Sheffield Wednesday trainee, who joined County in 2024, becomes the latest player to commit to the 2026-27 season at Rodney Parade after midfielder Harrison Biggins signed on a permanent deal.
It comes after three players - Bobby Kamwa, Matt Baker and Michael Spellman - turned down new contract offers from County.
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