He had to wait until 25 November that year for his Brighton debut, at the Goldstone Ground against Preston North End.
At Brighton he was converted to a wing half or full-back, and eventually made 195 league appearances, scoring six times, before moving to Torquay United in July 1967.
He immediately settled into the Torquay first team at the start of the season, but lost his place when Bill Kitchener was signed on loan from West Ham United.
However, Baxter regained his place in the first team when Kitchener was switched to the centre of defence after the career-ending injury received by Torquay defender Alan Smith.
In September 2001, Baxter, still a Torbay resident, returned to Plainmoor as a match summariser for BBC Radio for the game between Torquay and Scunthorpe United.