Gary Woods, a goalkeeper signed from Kilmarnock, joined Exeter City at the conclusion of a busy January 2023 transfer window. Starting as a trainee at Manchester United, he had previously appeared for a number of clubs including Doncaster Rovers and Hamilton Academical. 

Gary, a member of Cambridge United's academy when at school, joined Manchester United as a scholar/trainee in 2007. Released at eighteen, he signed a professional contract with Doncaster Rovers with whom he won promotion and made 73 league appearances. He then moved on to Watford, Leyton Orient, Ross County (loan) and Hamilton Academical. 

Gary appeared in over ninety league and cup games for the Accies in three Scottish Premiership seasons before moving on to Oldham Athletic, Aberdeen and, in summer 2022, Kilmarnock where he was employed as goalkeeping cover without making an apprearance. 

Signed initially on a deal until the end of the season, Gary made his first start for Exeter City on 11 February 2023 at Burton Albion before suffering an injury after six appearances. Making just one futher appearance towards the end of the season, he agreed to a contract extension into the 2023/24 season.

Starting the new season as back-up to loan signing Viljami Sinisalo, and with City's other 'keeper Harry Lee on loan, Gary played in the league game against Leyton Orient on 9 September 2023 when Sinisalo was involved with the Finland national squad. Appearing in the heavy defeat in the EFL Trophy against Reading ten days later, Gary then faced additional competition from Shaun MacDonald and was not named in a 'matchday' squad beyond mid-October 2023.