[6] In January 2012, Aberdeen manager Craig Brown confirmed that English Premier League club Fulham had expressed interest in signing Grimmer.
"[13] Four days later and an injury crisis meant that he started in an inexperienced centre-back partnership with 20-year-old Joe Davis as Vale lost 2–0 to league leaders Brentford at Griffin Park.
[15] He scored his first professional goal with a header in a 1–0 win over Oldham Athletic at Vale Park on 18 January and was named on the Football League team of the week.
[18] Fulham recalled Grimmer on 27 March 2014 by exercising a clause in the loan agreement, as manager Felix Magath wanted to cover for some defensive injuries.
[21] He was persuaded to join the "Shrews" after hearing good things about the club from his friend Fraser Fyvie and being told by manager Micky Mellon that he would fit in with the style of football at New Meadow.
[26] He made his second debut for the club five days later, as he helped Shrewsbury to keep a clean sheet as they beat Cardiff City 1–0 in the FA Cup third round.
[27] On 30 January, in the next round at home to Sheffield Wednesday, he headed an added-time winner in a 3–2 victory, after Shrewsbury had trailed 2–1 with five minutes remaining.
[34] On 6 January 2018, he scored the winning goal from long-range in Coventry's 2–1 victory over Premier League side Stoke City in the Third Round of the FA Cup.
[39] On 22 July 2019, Grimmer signed a two-year contract with League One club Wycombe Wanderers after impressing manager Gareth Ainsworth on trial.
[40][41] He later said it was an unpleasant experience to spend over two months as a free agent, but that "holding off for the right club was absolutely the right decision for my happiness and my enjoyment of the game" and he was "very, very thankful that I am where I am now".
He went on to start all three play-off games, as Wycombe secured a place in the Championship after beating Oxford United in the behind closed doors Wembley final.
[41] His fiancée, Sammy, speaking two weeks later, said that "I'm so proud of him and Jack won't let his winner's medal out of his sight – he even took it on holiday with us and we had to keep it in the safe at the hotel".
[45] He scored his first goal for the "Chairboys" on 11 January 2022, joking after the game that it was "quality over quantity" as his curved strike secured a 2–0 win at Bolton Wanderers.
[58] Grimmer was described as "tenacious, aggressive, intelligent, accomplished on the ball and rarely makes a mistake" by the Staffordshire Sentinel in February 2014.